What evidence leads to and supports the Big Bang model? A good review of the resulting expansion (and calculated rates) and ages derived from these observations can be found in a Scientific American article (October, 1998; pp. 92-96) prepared by Dr. Wendy L. Freedman.
Two accepted lines of proof for the Big Bang, already described, are restated:
1) The details of the creation physics and progressive emergence of various elementary particles during the first minute
of the Big Bang (the Standard Model and its variants; see page page 20-1) are consistent with a model
based on Big Bang precepts; these particles are the outcome of a history that can be predicted and explained by Quantum and High Energy Physics, that is, the theoretical production
and sequence of particles seems verified by the observed
amounts of H, He, and Li atoms in the Universe; and
2) The observations, particularly from HST, of the farthest galaxies as being more primitive in appearance and development -
are precisely what is expected from the expansion
model in which those parts of space (in which the galaxies are embedded) that have moved the fastest are now the most distant. Thus, we see them in earlier stages of evolution when they were younger as we look back in time outwards from our frame of reference,.
But, even more convincing are two other physical
observations that are best explained by a Big Bang
origin for the Universe, especially in terms of its
expansion behavior: redshifts of light (towards longer wavelengths) from
the stars as a composite source in galaxies and cosmic
background radiation.
In the 1920s, Edwin Hubble made revealing observations through optical telescopes. Using Cepheid stars as distance indicators he found that some of these were much farther away than any of those in the Milky Way. He knew the following about Cepheids in the M.W.: 1) they brightened and dimmed in a regular pulsating way, and 2) the higher the frequency of pulsation, the brighter (more luminous) the stars were in their radiation output (since distances to other stars adjacent to the Cepheids were fairly well known [see below], the luminosity of the Cepheids could be deduced). These two plots establish these ideas: As early as 1924, Hubble had found Cepheids in a great cluster of stars we know as the Andromeda galaxy. When he applied the period-luminosity relationship to these Cepheids, they were notably dimmer (less luminous) than he expected. The most logical conclusion: the host Andromeda galaxy was much farther away (hence, the relative dimming) than any stars in the Milky Way, whose size had been established as about 100000 light years. Thus, the Andromeda collection of stars had to be a galaxy beyond the Milky Way. This deduction is one of the great achievements in Astronomy and all of Science for that matter. Relying on more Cepheid measurements, by 1929 Hubble had observed various galaxys that were less than a billion light years from Earth but outside the M.W. Here are the data he published then:The Hubble Law and the Cosmological Redshift
Working with others, he extended his observations to even farther distances, publishing this plot in 1931:
Comment: This discovery was worthy of a Nobel Prize. But in those days, Nobels were awarded for Physics but not Astronomy. Hubble championed the cause to change that and after his death, astronomers became eligible for this prize.
Hubble's other great discovery is the now strongly confirmed fact that the velocity of expansion (of the Universe) is directly proportional to its distance from the point of observation (for us, on Earth or in nearby space).
Hubble noted that, as recessional velocities Vr were measured
for stellar sources over the range of astronomical
distances D that could be measured accurately at that time, the plot of Vr/D disclosed
a straight line relation whose slope has a value H,
known as the Hubble Constant, named after him.
This, the Hubble Law, is the fundamental statement of the Big Bang model. We repeat here his first published plot of velocity versus distance.
The resulting straight line plot is easily described mathematically, in the basic Hubble equation: The scale constant is designated by the letter H, and is called the Hubble Constant (stated as H0, which refers to the present day value; H has been different in the past). It is normally given the units of Km/sec/Megaparsec (an alternate form is Km/sec/million light years). The current value for H0 is 71.4 Km/sec/Megaparsec or 21.5 Km/sec/million light years). The uncertainty in the value is about +/- 10%.
The prime information derived from this equation is that objects (such as galaxies) appear to travel at ever increasing velocities as their distance from the observer (Earth) becomes ever greater. The upper limit to expansion rate is the speed of light (although some interpretations of inflation suggest that this huge leap in dimensional enlargement occurred at greater than light speed). The current rate of expansion is specified as one light year per Earth year (think about this and its logic should be revealed).
Note that the units for H are in velocity per specified distance. Thus, the velocity at one million light years is 21.5 km/sec; this means that a galaxy at that distance from Earth is moving away from our planet at that expansion speed. At two million light years it is 2 x 21.5 or 43 km/sec, and so on. If the Universe is indeed 13.7 billion years old, the velocity of the farthest observable galaxies, formed about 13 billion years ago would seem to be 1300 x 21.5 = 27950 km/sec. However, such a calculation is not straightforward since H has varied with time. Not only has H really changed to other values in the past, its value as determined by astronomers has changed in the last century. In the last 20 years, with the advent of space observatories, the range of values have converged on the presently accepted number. This graph shows this history: One problem troubling Hubble in the early years after his discovery is that when he used the first value for H he derived to calculate the age of the Universe, it came out around 2+ billion years, a number in stark conflict with the then accepted age of the Earth at about 4 billion years. The contradiction resulted from very imperfect - and too small - estimates of distance to the nearby galaxies he used. As more trustworthy values were obtained, and elliptical galaxies further out were better fixed as to distance, an improved curve resulted (but still applicable to redshift z values [see below] of less than 1). The diagram below is a recent plot of galaxy velocity (in km/sec; converted to kph by multiplying by 3600) versus distance (in megaparsecs) of each galaxy from Earth; the green dots denote specific galaxies for which "reasonably good" measurements have been made (other galaxies have also been so measured but their values are not on this diagram).
Most of these values come from galaxies 5 billion or less light years away. H0 is the present-day Hubble Constant whose precise value is still a major goal in cosmological research; its spread of estimates is related to the uncertainties both in determining the redshift and in fixing the distance of a galaxy at the time light now received left it.
The Hubble Law works best (gives a straight line) from
plots of V versus D involving galaxies a few billion
or less light years away; uncertainties as to the
correctness of distances further out cause an increasing scatter of points
in the plot that suggest (or mask) some degree of
non-linearity related to the cumulative effects of
the curvature of space.
Although called a "constant", H has in fact varied in value over time. In this, it behaves much like the three non-linear plots of R (Scale Factor) versus time shown on the previous page. R describes how distances (as a measured parameter) change over time; H relates distance traveled in a unit time span (usually either Megaparsecs or million years) at each distance moving outward from the point of observation. The two are related. H refers to the relative rate of change of R. The reason that H has different values going back through the past is that it is unlikely that the expansion rate of the Universe has itself been constant since the Big Bang. One model of expansion was strongly influenced by deceleration due to gravitational forces pulling back on the enlarging universe, which means the rate of expansion has been continually decreasing, giving rise to a systematically changing H over the past (its value would increase as we move back in time towards the outer Universe). But now, new evidence for a gradual acceleration about midtime in the Universe's history (see next page) would also affect the variability of H. At best, we can now only determine with reasonable accuracy the value of H0, which proxies for the current value that takes into account the variations in earlier eons of the Universe. We can also say that H was at its maximum value relative to the present right after the extremely large (anomalous) expansion rate of Inflation; we cannot measure this value since we are unable to determine any redshifts until the Universe became transparent.
Hubble was led to the Velocity-Distance Law by interpreting the observed redshifts of stars and galaxies. To appreciate this, we need to explore in more detail what redshifts are. The concept of "redshift" has been mentioned several times on earlier pages in this Section. Redshift measurements have become the best indicators of cosmic distances - how far away are the stars and galaxies observed through telescopes (see next subsection for a discussion of how these distances are determined). These distances are inputs in calculating the rate of cosmic expansion. There is a systematic relationship between relative velocities of sources of radiation (such as galaxies) as these recede ever faster at increasing distances from Earth and the measured wavelengths of spectral lines from these sources. This is manifested as the redshift - so-called because light from a given wavelength such as in the UV and blue experiences a systematic decrease in frequency (ever longer wavelengths) towards (and beyond) the visible red as expansion velocities increase (this concept is discussed below on this page). As an example, the Lyman Alpha (Hydrogen) spectral line (see page 20-7) normally measured at 1216 Angstroms (in the far UV) when "at rest" on Earth is shifted to 9160 Angstroms (in the near IR) for a galaxy whose redshift is 6.54.
The redshift phenomenon was formalized by V.M. Slipher in 1912 but, in fact, H. Robertson noticed
a bit earlier that the farther nearby galaxies were from
our telescopes, the greater was the redshift. However, Edwin Hubble in 1924
has received credit for promulgating this redshift-velocity-distance
relationship because he included many more galaxies
as data points. He thus is recognized as the key individual behind the Expanding Universe model, from whence later came the Big Bang conception of its origin. (Note: Hubble himself never completely accepted the implications of his observations and had doubts about the Big Bang and most of the Universe models described below; for many years after drawing attention to this phenomenon he continued to prefer a Steady State rather than an Expanding Universe, although his position on the latter "mellowed" near the end of his life.) The Hubble Law can be formulated in terms of the redshift value z (where z is the recessional velocity divided by the speed of light; see below) for any celestial object (almost always a galaxy), thusly:
Some of Hubble's observed redshifts led
to estimates of galaxy velocities centered around 24 million kph,
about 2% the speed of light. Galaxy velocities vary, as indicated in this histogram. Some galaxies can go as fast at 0.1 light speed; a few even faster.
Let us now look into the details of the concept of "redshift". Redshift is analogous to, but not the same as, the familiar Doppler shift as applied to sound. Increases in recessional velocities are associated with changes in the wavelength of light being received, such that as the velocity becomes greater the wavelength becomes longer, i.e, moves to higher values (say, from 0.4 to 0.6 µm in the visible; wavelengths in other regions of the EM spectrum also are shifted towards greater values). This change is very much like the Doppler effect studied in Introductory Physics: this shows the influence of motion towards or away from the observer of a signal of some given wavelength, resulting in a systematic wavelength shift. One manifestation of a wavelength shift's effect,
which can be experienced in everyday life on Earth,
is exemplified by an audible phenomenon - recall the
sound of a whistle or horn on a fast-moving train
as it approaches and then moves past where you are
stopped at a crossing. Or, perhaps more familiar is the change in pitch of a steady ambulance siren as it approaches you and then falls systematically as the ambulance recedes after passing (lower frequencies). This wavelength
shortening (higher pitch) on approach and lengthening
(lower pitch) with recession is called the Doppler
effect, which results from velocity and/or position
changes (relative motions) between moving source and
stationary receiver.
In a sense, the lengthening of wavelength as light sources (mostly galaxies) recede from Earth at progressively increasing velocities and distances is seemingly analogous to the above Doppler effect. But, strictly speaking, this familiar effect as observed by us on Earth is not the same as applies to cosmic distances (although it is a good approximation for nearby galaxies in relative motion away from our observing location).
As applied to more distant objects seemingly moving away from us during Universe expansion, the wavelength shift actually results from a different mechanism known as the Cosmological Redshift. From a relativistic standpoint, while Dopplerlike in its
consequences, the cosmological redshift is analogous to
the "stretching" of light caused by the progressive
increases in distance resulting from the continuous
expansion of (curving) space. This in turn results
in proportional increases in recessional velocities
(thus in the formula for velocity v = d/t, it is the
d that changes with respect to steady time progression)
with increasing distance from Earth (recall the rubber
band analogy on page 20-8).
The causative influence of expansion resulting in a stretching or elongation of wavelength is evident in this diagram: A recently reported observation of a type of galactic body called a HERO (Hyper Extremely Red Object) may be the result of this cosmological redshift. Check these two images: On the left, the object is not detected in visible light; but it appears as a red blotch in the near Infrared. The object, at least 10 billion light years from Earth, has been found to be speeding away from us at nearly the speed of light. One interpretation considers this object to be red (from a large proportion of older stars) at the time its light left the source 10 b.y. ago . But another considers this object to be composed in large part of bright, bluish stars, perhaps even farther away (13 billion l.y.) but owing to the cosmological redshift the light as received has been stretched to near Infrared wavelengths (but assigned red in this false color rendition). Redshift phenomena are effectively studied from the spectral states of starlight (see page 20-7). As a star or galaxy emitting radiation recedes from
an observing (measuring) spectrometer (somewhere on
or near the Earth), the wavelength associated
with a particular line will
be shifted towards the red (longer wavelength-lower energy end
of the visible spectrum) and even into the near Infrared. What is measured is the displacement (δλ/λ = the incremental wavelength shift ratioed to its initial wavelength λ) of this line to a new apparent wavelength relative to its [rest state] wavelength in a spectrum obtained by exciting
the element on Earth in an emission or absorption spectrometer. Before modern electronic measuring methods, the spectra were commonly recorded
on a photographic plate showing multiple lines that
result from the spectral spread of wavelengths characteristic
of all detected elements) representing an element in
its ground or some excited state in the visible. The diagram below shows four sets of spectra, for hydrogen, with the bottom representing a star in the Milky Way, and each successive spectrum upwards representing galaxies at increasing distances from Earth. The leftward shifts are towards longer wavelengths.
This next illustration shows telescope images and spectra from five galaxies at increasing distances from Earth.
This oft-cited diagram, traceable to Hubble's work, can be misleading without some interpretation. To pick out and thus intrepret these spectra, start with the Virgo galaxy example (top right). The top and bottom lines are the same emission spectra for this spectral interval (unspecified as to Angstrom units; the lines are white instead of black because the photographic plate is printed as a negative) obtained by spectroscopic analysis on Earth of a sample containing elements observed in stars . The two leftmost lines are the H and K spectra for the excited Ca++ state. The spectrum from the galaxy appears as a long lenticular white smear in the middle between the two reference spectra. The vertical arrow points to the now shifted H and K line pair, which here appear black because they are absorption rather than emission lines. In the spectral image second from the top, the horizontal arrow leads to the position of the line pair (which does not reproduce well on this page) for a galaxy in Ursa Major, now shifted notably to the right. In the three succeeding spectal images, the horizontal arrow carries to the position of the two (hard to see) dark H and K lines after each greater redshift. From these observed shifts, the recessional velocities listed under each spectral image have been calculated. These could be plotted on the distance-recessional velocity diagram above, and would fall within the general distribution shown thereon. Today, the spectra are more commonly recorded as continuous tracings on a strip chart. The next figure shows a spectrogram recorded by a Kitt Peak National Observatory telescope in which the top spectrum (obtained at rest in the laboratory) has peaks for three Hydrogen lines at 4340 A (in the blue); 4860 A (green) and 6552 A (red). The next four are spectra from distant quasars at progressively greater distances. The displacement of a spectral line owing to redshift can be used to calculate the Cosmological Redshift value z associated with a source simply from the rest wavelength of a given line and the observed wavelength of the same line displaced by the source's motion.
The Cosmological Redshift z is given as:
Using the z value, the velocity v of receding motion of the source is given by:
Since the redshift is velocity dependent, its magnitude
is a direct indication of the rate of recession, i.e.,
the larger the shift, the greater the velocity. The redshift z is a number that represents the fraction by which spectral lines from a luminous source shift towards longer wavelengths. Values of z range from less than one for closer sources and have risen for the most distant sources (early time galaxies) to numbers around 6. If instead the source advances towards the observer,
the shift will be towards the blue (shorter wavelengths). Since it is postulated in the Big Bang model that all sources are apparently moving away from one another, a blueshift would seem anomalous. However, this occurs, for example, when spectra are acquired from a rotating spiral galaxy in which arms on one side (from the center) may indeed be moving away but the other side must be approaching from opposite directions. Likewise, some galaxies in a local group may appear to be moving towards Earth towards Earth, but the entire group is still receding relative to our galaxy.
Another mechanism can cause redshifts, namely, the
effects of gravity on radiation. This gravitational
redshift is a consequence of General Relativity.
When light leaves a massive gravitational source,
such as a White Dwarf, gravity causes a shift towards
a longer wavelength (conversely, light passing into
a huge gravitational field will undergo a blueshift). The massive body thus slows down photons representing a range of energies as these escape from it, causing a loss in their energies that results in reducing their frequencies and increasing their wavelengths.
This effect has been observed for light grazing supermassive
bodies, including Black Holes. Overall, the effect
is localized or confined to individual bodies, and
normally the shift is very small, so that even the
cumulative effects of light reach Earth from the outermost
reaches of Space are quite small compared with the
motion-induced Cosmological Redshifts related to expansion. Nevertheless this local redshift must be accounted for when individual receding galaxies are used in determining the cosmological-scale redshifts.
There is another, more general effect of gravity, shown in the plot below, which shows the redshift curve for a Universe with maximum gravity influence versus no gravity at all. The ordinate is distance in billions of light years. This range of possibilities is pertinent to the accelerating Universe model discussed on the next page. Most redshifts measured so far include the lower values of z obtained by examining a range of "normal" galaxies at distances from Earth under about 7 billion light years.
As stated above, most redshifts are observed to fall within the range of a fraction of 1 to about 3. These are all associated with galaxies that are less than 10 billion years (in lookback time) from Earth. This is evident in this plot: As galaxies lying beyond 10 billion light years are observed, their redshifts begin to rise at more rapid rates. Thus: The ordinate denotes relative age: The present time is given by "1", with nearby galaxies that appear most fully evolved (to us in the present time) having very low redshifts. The exponental drop in the curves (the red curve applies to a Universe with 70% Dark Matter; the blue curve described a Universe without Dark Energy [Cosmological Constant = 0]) shows that the maximum rate of increase in the value of 'z' occurred when the Universe was less than a relative 0.2. Higher redshifts have been found for galaxies that are strong radio sources and even larger values (around z = 5 to 6.5) from very distant quasars (mainly those which display their effects in the first two billion years of Universe history). Values of 'z' increase rapidly towards infinity for Universe events older than the first stars. For instance, at the time of Recombination (page 20-1) z = 1000. This is the general relationship as tied to major cosmological entities: The most distant galaxies are hard to observe but their redshifts can be greater than 10. Theory permits calculations of redshifts from the Recombination Era back through the first minute of the Big Bang. These values have been taken from Joseph Silk's The Big Bang (3rd Ed, page 68): At Universe age of 2 billion years, z = 5; Decoupling at 380000 yrs, z = 103; Radiation Era, 1st minute after the BB: z = 109; Hadronic Era, at t = 10-10sec, z = 1010sec; Planck time, at 10-43sec, z = 1032 ; Now with this overview of redshifts, the reader is encouraged to work through a review on this Wikipedia website.
To calibrate and then apply the redshift to estimate R (Scale Factor; previous page), and to calculate the Hubble contant H,
the distances to the stellar bodies each with a specific redshift must be determined. Over the last century various methods of estimating distances have been developed. A good, in-depth review of the principal methods used in distance determination is found at
Ned Wright's Cosmology site.
Some of these methods will be discussed in this subsection. Use of multiple
methods applicable at different distances is called
the Cosmic Distance Ladder. We will start with an overview given in these two illustrations and a summation:
This is a synopsis of most of the distance measuring methods: 1) .For the Solar System: Radar is the most accurate measuring method. 2) For nearby stars: The parallax method, using either Earth's orbit to occupy different positions or an orbiting satellite, to determine how far away are stars in the Milky Way Galaxy; works well out to about 3000 light years. 3) For some stars farther out in the Milky Way: The standard candle method uses stars whose true luminosity L can be determined. 4) For stars out to the edge of the Milky Way: The Cepheid Variable star method is employed. 5) For many more distant galaxies out to several hundred million light years: The Tully-Fisher method utilizes measured brightness and galaxy rotation (using the Doppler effect). 6) For galaxies out to about 10 billion light years: This depends on observations of White Dwarf supernovae, whose intrinsic brightness is well known. Some of these methods have accuracies of +/- 10% or better. Now, to more detail: Distance measurements obtained for nearby bodies,
e.g., in our own Milky Way galaxy, can be made on
visible stars whose magnitudes can be directly ascertained.
One technique is that of parallax observations. While
not fully explained here, the gist of this technique
can be sensed by this simple experiment: Hold your
index finger first about 6 inches in front of your
nose and rapidly alternately close your left eye and
then right one repeatedly. Your finger will appear
to shift back and forth relative to a fixed background,
perhaps seeming to displace several inches. Now, put
your finger full out (about 24 inches) and do the
same thing. Note that the displacement is now less.
This is the parallax effect (first discussed in Section 11). The amount of shift decreases
with increasing distance and that distance can be
determined by simple trigonometry.
As used to measure
stars within about 100 parsecs (326 light years),
the left and right eye positions are proxied by the
positions at opposite points in the Earth's elliptical
orbit six months apart. A star's apparent shift relative
to distant background stars, even though proportionately
much smaller than that of the finger experiment, is
sufficient to provide an accurate distance measure
for stellar bodies close to Earth.
The standard candle method requires use of objects (stars; galaxies) whose intrinsic luminosity L is known. At some distance d, the L (in watts) is spread over a sphere of area A = 4πd2. What is actually measured is brightness b; b = L/A. The distance d is then calculated as d = (L/4πb. Approximate distances to closer host galaxies containing separable stars rely on determining the intrinsic luminosity of certain types of individual stars. One class is the so-called pulsating stars, i.e., those whose luminosities vary systematically over periods of days to several months. These include stars that have used up nearly all of their Hydrogen fuel and are enroute off the Main Sequence towards then becoming Red Supergiants. During this phase of their history, their atmospheres expand rapidly with a rise in luminosity, only to revert back to their previous state during a cycle whose time is that of a regular period. What happens is this: the star in its more compact state has a specific internal pressure; at some point the nuclear processes cause the star to expand, increasing its diameter by a factor around 2. The pressure gradient decreases until a condition is reached in which gravity now reverses the process causing contraction. The expansion-contraction repeats at its characteristic, nearly constant time period (in Earth days) for a long time before a particular pulsating star evolves into a more stable Red (Super)Giant. Most stars showing this phenomenon have initial masses from 5 to 20 times that of the Sun. More massive stars have longer periods of expansion-contraction and are also more luminous to start with.
One class of periodically pulsing star groups are the RR-Lyrae stars whose periods are in hours to a single day. More important are the Cepheid Supergiant stars. Cepheids were first discovered
by astronomer Henrietta Leavitt in 1912 in the nearby Magellanic Clouds; she then showed them to have regular, pulsating variations in luminosity proportional to their pulse periods (in so doing, determined that the brighter the star, the longer its period P). Cepheids flare up to peak brightnesses, then dim down, over periods of days to weeks. Using the parallax method, the distances to some of these were independently fixed and their absolute magnitudes M were calculated. Since these distances varied (within the Milky Way and in the Magellanic Clouds), the various M values could be associated with their corresponding periods in the cycle, thus establishing the M-P relationship. Of course, Cepheids having the same values of M but located at widely varying distances from Earth will experience an apparent decrease in brightness m depending on distance (and subject to the 1/d2 relation that defines the falloff in brightness with distance). These ideas are illustrated for one type of Cepheids (δ-Cephei) and for the more general case:.
Once absolute luminosity for a given Cepheid is calibrated from this relation, the drop in apparent (observed) brightness m from that value owing to its specific distance d can then be included in the following equation to determine that distance to this star:
In the 1920s, Edwin Hubble firmly established the relation
that the longer the period, the greater is the increase
in the intrinsic (absolute) brightness in a Cepheid.
He applied this pulse cycle approach to these stars in different galaxies and over a range of distances. It was Hubble's use of primarily Cepheid-derived distances that led to his first major hypothesis of an expanding Universe, after also introducing the redshift relation. Some of the values he used were not highly accurate (but were later corrected) so that his initial postulated rates of expansion were considerably off-the-mark. The Cepheid variable star method works well out to a distance of 50 million
light years (roughly, out to Virgo). For galaxies farther away, other methods of measuring distances to them (such as the rich cluster-brightest galaxy indicator which gives usable approximations out to 10 billion l.y.) have been worked out and applied (these have varying degrees of accuracy.
The best among these is the Type Ia supernova explosion (discussed in more detail on the next page). This occurs when a white dwarf star has a larger binary companion. Material stripped from the larger star accumulates around the dwarf until a critical mass (~1.4 solar masses) is attained, at which point it explodes releasing luminant energy of a narrow range of L. (Details about White Dwarfs are presented on this Wikipedia website). Thus it qualifies as a standard candle star. This explosion is a Type Ia supernova that is so bright that it is readily detected in very distant galaxies. This plot show the relation of luminosity to time history of Type 1a and Type II supernovae:
This next diagram was shown first on page 20-1. It is repeated as a summary of some of the Cosmic Ladder methods: As earlier stated, cosmic distances are used to relate redshift values to recessional velocities. When redshifts begin to exceed about 1, the speeds of the objects concerned begin to approach relativistic values, i.e., they are ever larger fractions of the speed of light. Thus, although the actual speeds continue to increase, the incremental rate of velocity increase itself decreases (slope asymptote approaches 0). This gives rise to a redshift vs recessional speed curve that is like this: Another relationship:
z = 1/R(tem) - 1 describes the redshift
in terms of the Scale Factor R pertinent to tem
which refers to the particular time when the light
was emitted . This relationship can also be cast in
the following way: 
From Astronomica.org
Vr (velocity of recession) = H0 x D (distance)
From: Misconceptions about the Big Bang, by C.H. Lineweaver and T.M. Davis, Scientific American, March 2005
ILLUSTRATIONS COURTESY OF ALFRED T. KAMAJIAN
From J. Silk, The Big Bang, 2nd Ed.
Source: M. Corbin
z
= ( 
rec -
em)/
em = Vr/c, = H0r/c
em is the wavelength of EM radiation given out in the past
(then) at the emitting galaxy or star, rec
is the shifted wavelength received today (now) at
the detector (on Earth), Vr is the recessional velocity
for the particular redshift, c is the speed of light, r is the distance to the star whose redshift is measured, and HO is the Hubble Constant..
The above equation applies to low to moderate z's
but for large z's, which are attained as the velocities near that of light speed (and are characteristics of the early moments of the Universe) a modified expression must be used:
z + 1 = (1 + v/c)/(1 + v2/c2)1/2
v = cz (1 + 0.5z)/(1 + z)
Stellar and Galactic Distances (from Earth)
m - M = 5(log d/10)
From Astronomica.com
in which Dnow is the distance to the emitter
when the light is received and Dthen refers
to the distance in the past when light left the emitter.
A plot of z + 1 versus r/R (the distance out to any galaxy ratioed to the distance out to a Universe's edge, set at the Scale Factor R) shows the exponential character of this curve (generalized here):
We see a redshift (towards longer wavelengths) because
the Universe had a different Scale Factor when the
light left the emitter. The redshift is due to the
relative expansion of space (increasing "D's"
[for distance]) rather than actual speeding up of
more distant galaxies. Look at the two circle drawing
shown earlier on page 20-8. Note the S-like curl that represents part of a wavelength train. It has
a shorter wavelength in the left circle; as the circle
expands with its enlarged coordinates, note that the
wavelength on the right is now longer.
Before new data from the HST and other observing systems were acquired, the prior estimates of the value of H0) had fallen
between 50 to 100 km/sec/Megaparsecs (a parsec
is 3.26 l.y). (In some expressions of H, megaparsecs
are replaced by 1 million (106) light years;
thus 75 km/sec/Mpc = 23 km/sec/106 l.y.)
One goal of the Hubble Telescope is to better zero in on
the most accurate value of H0 - essential to an accurate estimate of the Universe's age. From most recent best estimates, a range of H0 (value at the present time) between 65 and 79 km/sec/Mpc is considered the most likely to contain the eventual most accurate value (still being sought).
A good discussion of some of the above information on the Hubble Law is found at these two Wikipedia-1 and Wikipedia-2 sites.
The Hubble constant H0 provides a direct way of estimating the time from the Big Bang (Universe's "birth") to the present. Currently, 13.69 (rounded to 13.7) billion years (using H0 = 71.4 km/sec/Mpc, based on WMAP data [see below on this page]), with an uncertainty of +/- 10%, is the most widely accepted value. The general relation for the Universe's age (since the Big Bang) is given by the expression:
This formula is deceptively simple. Just putting in a value for H0 yields a number that is not years as such. The proper units must be included. Here we will run through the calculation that leads to the end-result age for a value of H0 = 71 km/s/Mpc (s = sec; Mpc must be converted into mega-light years). In the actual calculations, when H units (in the Mpc mode) are adjusted to give an answer in billions of years, the formula becomes:
Inserting 71 km/s/Mpc into the formula yields an age of 13.7 billion years. Most textbooks on Cosmology and relevant Internet sites do not show the details of the calculations in regard to units involved. This is done here: The bold letters refer to units that cancel out. The lower the value of H0, the larger is t0 and thus the Universe becomes older; smaller H0 yield younger ages.
The
first reported (before 1995) HST-derived ages fell between 8-12
Ga, anomalously low compared with pre-HST reported
ranges of 12 - 18 Ga. This was especially confusing in that
separate evidence and theoretical calculations indicate some distant galaxies might well
be 14 Ga and possibly older. This Age Paradox - stars seemingly older than the Big Bang's start time - proved particularly troubling to cosmological theorists for several years. The problem was minimized with further studies of nearby globular clusters which contain very old stars. These clusters formed along with the organization of the oldest galaxies around which the clusters are tied by gravity within the galactic halos. Data from the Hipparcos astronomical satellite led to a redetermination of globular cluster luminosities, and correlative rates of fuel consumption. From this new information the average ages of clusters was reduced by 14% so that their oldest stars (Red Giants) could not be older than the 13 Ga cited above. This, together with the more refined 13-14 billion year Hubble age (see below), obviates the discrepancy posed by the Paradox. One consequence of this most
recent age estimate is that the farthest galaxies whose distances from Earth
is said to be 13.4 billion l.y. must
lie near the observable edge of the Universe. One galaxy has now been found at 13.23 b.l.y, and in time more will be detected that are even farther away (older).
Over the past 7 years, observational data analyzed
by HST Teams whose prime task is to try to pin
down the Universe's age using a better determined
Hubble constant suggested in May of 1999 a
best estimate for the Hubble constant of 70 km/sec/Mpc. (That number also coincides with the local expansion rate based on redshift-distance measurements for galaxies near the Milky Way.) For the H0 range they arrived at, an age of 13.97 billion years would result - a value reasonably close to the more recent WMAP results. The age uncertainty
represents an accuracy variation to within +/- 10%
for the value of this constant. Their value depends
on analysis of redshifts in 18 galaxies within 67
million l.y. from Earth; in these they have found
up to 800 Cepheid variable stars which are considered
reliable indicators of large distances. From the combined
determinations for the 18 galaxies, this best estimate
of expansion rate gives an increase in velocity of
256,000 km/hr (160,000 mph) for every 3.3 million
l.y. farther out the stellar entity (galaxy or individual
stars) is from Earth.
A group of astronomers associated with Marshall Space Flight Center colleagues have used 38 galaxy clusters spread over distances from 1.4 to 9.3 million light years observed by the Chandra (X-ray) Observatory space telescope combined with radio telescope data to obtain intrinsic luminosity data from which distances can be calculated. Using these, they derived a value for H0 of 77 (+/- 15%) which translates into an age of 12.7 billion years for the Universe. Many astronomers disputed the above age specifications based on the galaxy distance model, citing older ages according to their calculations and their interpretation of H values using different inputs. In the late 1990s most cosmologists (e.g., Alan Sandage and associates) had accepted
a small range of values of H0 that yield ages centered on 14 Ga; those ages are now close to the preferred "best estimate" of 13.7 Ga (see above). However, a vital note of caution: As more galaxies at great distances from Earth are detected and measured astrometrically, so that their intrinsic brightnesses, distances, and redshifts are known with notable accuracy, the value of H0 could be recalculated to a lower number. This would mean an older Universe (greater than 14 Ga) and would mean that the oldest galaxies now detected lie inside the limits of the knowable Cosmos. Said another way: there may be considerably more space beyond our present observable Universe, which is where our time horizon now extends, and this additional outer volume would likely contain galaxies. This can be assessed when/if we can see the outermost, already detected galaxies in such detail that we can specify how primitive or early they are in their evolution. If they appear to be in the first stages of formation, if we know enough about their rates of growth, and if galaxies indeed to form within the first billion years after the Big Bang, then these galaxies are probably near the edge of the expanding Universe, with little or no space beyond. This does not rule out an infinite Universe, if it is destined to continue expanding into an infinite future.
However, the Hubble Age also can be modified depending on whether the Universe is open, closed, or flat, and may be influenced by the type of space involved (see below). In the absence of gravity the value of tH is 1/H0. The Hubble age for a Universe with flat
expansion varies as the relation tH
= 0.67/H0 (this applies to the Einstein-DeSitter Universe [see below]). For an open Universe, tH falls between 1 and 0.67 but 1 is usually chosen; an open Universe seems the best model at this time. For a closed Universe, tH can be less than 0.67. These several cases for ages that are less than 1/H seemingly point to Universes that began less than ~14 billion years ago. But, if the ages of the most distant galaxies, now only estimated from distance-brightness relations, prove to be around that value, then the resulting paradox - parts are older than the whole - will need to be explained away. To some extent, resolving this paradox can help to specify the type of Universe that actually exists, since age-incompatible situations would seem to argue against the types that don't fit.
Just when it seemed that astronomers have finally firmly fixed the value of the Hubble constant so that the Universe's age and size can be considered as accurate, a new set of data - if confirmed by additional observations - have cast doubt on the best number for H0 and hence for estimates of Universe age and size. A group of astronomers led by Dr. Kris Stanek of Ohio State Universe have spent years developing a new technique for determining distances to galaxies and stellar objects that would avoid several steps in the process - hence reducing errors. Their method involves determining the mass of mutually orbiting binary stars, which allows calculation of intrinisic brightness that is compared with apparent brightness, from which distance is then established. They used two large bright stars in M33, the Triangulum galaxy. Their method came up with a distance from Earth of 3.0 x 106 l.y. Previously that galaxy had been rated as 2.6 million light years away. If, after repeated testing and detailed assessment by fellow astronomers, their method holds up and becomes accepted as the best distance estimater, this could imply that the 15% greater distance the OSU team found for M33 is valid for other galaxies at various distances. The value for H0 would need to be adjusted downward by 15% and thus cosmic age and size of the Universe would need to be increased by 15%. At the moment, the "jury is still out" on this new result. Nevertheless, from the above, variations in the chosen value for H0 have a major, definitive influence on two fundamental cosmological parameters that scientists seek to know "exactly" - the size of the observable Universe and the age of the Universe. This notion is brought home by considering the consequences of changing the H0 value, as is done in this figure: The question to ask in interpreting these H curves is which one leads to a younger Universe; which Universe is smaller? Check the conclusion by clicking on this asterisk *. The essential factors determining the Universe's age
are its overall density (mass and energy) and the
value of the Deceleration Parameter (related to the
Hubble Scale Factor), as discussed elsewhere on this
page. These specify the rate of expansion which in
turn reveals how long it takes for galaxies to get
to the farthest reaches of observable space
Observable space is defined as the limits or horizon defined as the farthest
bodies that have emitted radiation which has had time
since the beginning of the Universe to travel to Earth's
observing stations. This will be marked by the first
vestiges of materials capable of emitting detectable
radiation during the early moments of the Big Bang.
So far, detectors covering optical and other spectral
regions have not yet picked out these oldest sources,
so the currently observable Universe presently is
smaller than the total observable Universe.
The Hubble equation specifies that the fastest receding
objects must be farthest away; conversely, those near the Milky Way are the slowest moving. Thus, in an expanding Universe,
with all galaxies ultimately drawing apart from each
other, those progressively farther away must travel
at proportionately greater speeds, but at the same
rates in all directions, to preserve an overall uniformity
of spatial relations during these expansive movements.
As a general rule, the greater the lookback
time, the smaller was the size of the Universe at
such times, and the hotter and denser is the early
expansion status of matter and energy. (Lookback time connotes the idea that the farther out in space one looks, the further back in time [earlier] is the event or stage of development associated with objects [e.g., galaxies] when light left them; a large Lookback time means a younger age]).
Because most galactic measurements made on distant
galaxies show red rather than blue shifts (the latter
are seen for mostly nearby galaxies moving towards
us [Andromeda is approaching Earth at ~360,000 kph]
or can be noted in individual spiral galaxies as one
arm moves towards Earth), this evidence for overall
(net) recession is the principal proof for the Big
Bang expansion model. The redshift is related to recessional
velocities (ratioed with respect to the speed
of light) by an exponential curve in which the velocities
rise rapidly towards infinity as that speed in approached.
Most measurements of z from less distant galaxies
afford numbers between 0 and 1 (for example, z = 0.1 represents a distance of about 1 billion light
years). Farther out galaxies showing redshifts of
1.2 correspond to ages in light years of about 8 billion
years; HST has now observed many galaxies with z's
up to 2+. Distant quasars, some about 10-11 billion
l.y away, have shifts of 3 - 4 or higher (at an observed
age much earlier in Big Bang time). Several galaxies have measured z values of 5-6 and one now has a value of z = ~10 (reaching to about 90% of the speed of light); these are thus formed during the first billion years of the Universe.
Here is an image obtained during the Sloan Digital Sky Survey (SDSS) showing a galaxy with a redshift of 5.82 that is unusually bright (a quasar is inferred as the cause).
Recessional velocities as a function of distance
of cluster galaxies from Earth as the observational
frame of reference can be calculated from the
Hubble equation and z values. Choosing a Hubble constant
that gives 14 Ga as the age of the Universe, a galaxy
recedes an additional 25 km/sec for each million l.y.
further out one looks through space. For a cluster
in the Virgo Constellation, at a distance of 78 million
light years, the recessional velocity is ~ 1200 km/sec.
For the Bootes cluster, at 2.5 billion l.y., the velocity
has increased to 22000 km/sec. Galaxies whose distance
is about 5 billion l.y., attain velocities approximately
one-third the speed of light (100000 km/sec). The
most distant observed sources (mainly quasars) reach
recessional velocities approaching light speed. The
same type of velocity distribution would be ascertained
at any other observational point (such as set up by
the distant galaxy "civilization" referred
to earlier) in the Universe.
As HST observations accumulate, it is becoming evident
that, with its resolving power, structure in galaxies
can still be recognized out to about 4 billion light
years. Present evidence is that beyond a z value of
2.75 no well-formed spiral galaxies can be confirmed to exist (but at least some are likely). Those that
lie farther out seem to be ellipitical or commonly
"dismorphous" (no regular form). Since these are older,
this implies that spiral galaxies may not develop
until later in galactic evolution. Some of the earlier-formed
spirals have one or more extra arms compared with younger ones (the Milky Way has 3 major ones).
The discussion in the above paragraphs is confined to redshift measurements that can be made from observable astronomical phenomena such as galaxies and quasars. There is another aspect which is more theoretical, namely, the redshifts in the earlier history of the Big Bang prior to the onset of the Decoupling Era (before which no direct observations is possible). At the initial Planck Time of 10-43, the redshift z is calculated to be 1032. After one minute - the beginning of the Radiation Era, z drops to 109. In the first 1-2 billion years after the B.B., the redshift decreases from about 30 to 6. The latter is near the maximum value
determined so far by direct measurements - the galaxies with that value are about 13 billion l.y. away. This systematic increase in redshift going back in time accompanies the expansion of the Universe. The process of enlarging space leads to a lengthening of the wavelength of light - hence the progressive rise in the redshift value of z. Photons that have to travel greater distances, from further out in the expanding Universe, appear as though they have decreased energy - hence longer wavelengths (Planck's Radiation Law), i.e., shifts from blue to red. Since redshift depends on the velocity of a receding object, it follows that the maximum velocities of galaxies are found in the outer reaches of the observable Universe. This is logical: if all matter/energy was concentrated at a singularity at the time of the Big Bang and then dispersed thereafter, those manifestations of matter such as the galaxies that are farthest from the observation point (for us, Earth) must have been traveling at the fastest speeds - in other words, if all matter started from the same point, matter now farthest away had to travel at the highest velocities. There is also another theory which can, in principle, modify the implications of the observed redshifts, namely, that the velocity of light is not constant but has changed over time by gradually slowing down: this is the "tired light" concept which, while intriguing, has so far not been supported by data or observational proofs, although it does seem to have a relation to the expansion aspect of stretching light to longer wavelengths (paragraph above). It has its supporters; some cosmologists and quantum physicists have postulated that the current values of certain fundamental parameters have changed with time, having different values (especially in the early moments of the Big Bang) that evolve into their present numbers as the Universe grew. Even though evidence for this is presently lacking, this is not trivial or frivolous speculation but falls into the time-honored scientific methodology of proposing seemingly outlandish theorems or propositions capable of explaining some phenomena and then conducting experiments to confirm or deny the idea.
The age of the Universe is a fundamental value which cosmologists seek with great care and effort to establish accurately. What will help in settling on a "best value" would be an independent measurement using a technique other than the recessional velocity extrapolation. In April of 2002, a seemingly reliable second method has been reported. It is based on knowledge of the time involved in White Dwarf stars burning out their remaining fuel to reach a "glowing ember" state. Theory sets a fairly precise time span for this to occur. In the earliest stages of galaxy formation, Globular clusters will contain rapidly produced white dwarfs as large stars burn their Hydrogen over a brief time and then enter the Dwarf stage. The "embers" that are very old are hard to detect by telescopes. But, the Hubble ST has been used on a globular cluster near the Milky Way to search for these embers; by taking a long exposure image (cumulative 8 days, spread over 67 days) these faint White Dwarfs were detected, as shown in this set of images of stars within cluster M4: As reported by Dr.Harvey Richer and his colleagues, calculations place the age of these White Dwarf "cinders" at between 13 and 14 billion years. By adding ~1 b.y. (typical time for the first Globular clusters to develop) to these values, this independent age assessment falls right within the same range now generally accepted from recession measurements. The two methods of determining Universe age, using a "ladder" approach to arrive at the final values, are shown schematically in this diagram:
Unless fatal flaws are discovered in either or both methods, it seems for now that an upper limit of 14 billion years will stand as the actual age of our Universe. We can summarize the age information that includes key events in the Universe's early history by posting this diagram which includes some of these events (most of those were described on page 20-1): Note that we can only look directly back at stars and galaxies, such as those that formed in the early Universe, to a time approximately 380,000 years after the Big Bang. Another solid proof for the Big Bang was the discovery
that Cosmic Background Radiation (CBR; also referred to as Cosmic Microwave Background [CMB] radiation in the diagram just above) peaks near
the wavelength of 1 mm (1000 µm [micrometers])
which lies at the far IR/microwave boundary region
of the EM spectrum. This is the peak wavelength expected
from a radiant blackbody source whose temperature
is now 2.73° K. George Gamow and his colleagues Ralph Alpher and R. Hermann had first
predicted such radiation (their estimate of its peak
was at 5° K) in 1948. The term "afterglow" can be applied to this radiation. The radiation consists of photons (whose electromagnetic wavelengths vary with the blackbody temperature distribution at any given time after the BB) created during the first BB minute as matter and anti-matter annihilated almost completely.
The CBR now evident as pervasive throughout space (both intragalactic and intergalactic) can be traced to an equilibrium state between nucleons, electrons and photons that was arrived at when the Universe had cooled to about 10 million °K approximately 6 months after the Big Bang. Evidence of what it was doing during the Radiation Era, up to Decoupling, had been lacking because of the opacity brought about by scattering and internal entrapment of photons (see page 20-1) within the early Universe during the next 350,000 years. At that time, as the temperature dropped to about 3000 °K, almost all electrons (the principal scatterers) and protons were able to combine as Hydrogen atoms that no longer scattered the photons so that light and other radiation emerged from the radiation "fog" which was fully lifted by 1,000,000 years after the BB. With the resultant transparent Universe, CBR first became detectable, displaying the higher temperatures it then possessed in the still early Universe. (If anyone had existed at that time, a near-infrared radiation detector would have been needed since that was the spectral range for a temperature of 3000° K; the CBR had cooled through the temperature range that would be in the Visible while the opaque Dark Age still dominated.) From Decoupling to the present time, the CBR has experienced a redshift of ~1200. This relativistic redshift resulting from expansion is involved in causing the temperature of 2.73° K that is recorded today.
The photon radiation throughout the Universe now being measured is a manifestation of the present-day Cosmic Microwave Background (CMB), inherited
from the original radiation (much hotter and therefore
then of much shorter wavelengths in the Infrared)
released at the Big Bang. Astronomers commonly refer to the CMB as the general residue of photons that were produced and released during particle interactions in the first minute of the Universe - colloquially, the CMB is the remnant of the "burst" of radiation that marked the "explosion" of the Universe (but which really didn't explode in the sense of detonation of a nuclear device in which there is an initial "flash" of light). It is also referred to as the "afterglow" of the BB. This radiation seems to be very uniform and isotropic throughout the Universe. The vast majority of all photons found in the present Universe are tied up in the background radiation. However, despite their huge numbers, it is estimated that they comprise only about 1/50000th of the mass contained in all the galaxies. The present ~3° K value is consistent with a predictive model that requires very energetic high temperature radiation (mainly gamma rays, with
much shorter wavelengths) that constituted the early CMB released soon after the Big Bang to cool drastically by adiabatic (no energy added or removed) thermodynamic expansion (a good Earth analog: expansion of an air mass is accompanied by release of heat with resultant cooling)
within a Universe having at the least the presently
observed spatial limits. Mechanistically, as space is stretched the original shorter wavelength photons experience a corresponding lengthening of their wavelengths into the microwave region and so lose energy (E = hc/λ) which in turn is expressed as a much lower temperature. The extraction of a weak radio telescope signal (after
receiver noise was subtracted) in the microwave region
at 7.3 cm (4.1 GHz) was made in 1965 by R. Wilson
and A. Penzias (for which they received the Nobel
Prize in Physics; their discovery was somewhat accidental at first since they were trying to track down what they perceived as "noise" in their radio telescope). (Actually, a similar signal was first detected
in 1961 by E. Ohm, then verified by B.Burke, but not
connected to the CBR prediction.), with its correlation
to cosmic background radiation. Correlation of Wilson and Penzias' discovery and its implication for the predicted background radiation was then confirmed by R. Dicke and his group at Princeton.
This accomplishment, along with the work by Hubble, the theory of General Relativity by Einstein, the pioneering concepts of a primordial singularity by Lemaitre, the Inflationary Model by
Guth, and supporting contributions by numerous cosmologists,
astronomers, physicists, and mathematicians, taken
together, make up the foundation concepts
that support and explain the Big Bang in its present
form. Further discoveries will likely lead to refinements
but the fundamental premises and the proper numbers
predicted from the general model now seem to be solidly
substantiated.
The value of satellites in understanding CBR is well illustrated by COBE (Cosmic Background Explorer), launched in 1987 (check out its current COBE website. Earlier attempts by Smoot and others
to map the apparent non-variant (uniform) background
radiation over the entire sky using balloons and aircraft,
to make measurements above the atmosphere which blocks
out (absorbs) radiation in the .001 to 0.1 m wavelength region
of the spectrum, gave strong hints of radiation uniformity
but were subject to imprecision. With COBE, the mapping
process was greatly improved so that a detailed chart
covering the full sky was assembled in just a year.
COBE verified the high degree of uniformity of the
present background in all directions and also confirmed
that the general expansion is extremely uniform in
all directions.
COBE took extremely accurate
readings over much of the wavelengths involved in constructing a blackbody radiation curve. These measurements were then combined with those covering other wavelengths and obtained by different means to produce this classic blackbody radiation curve (see page 9-2 for a review of blackbody radiation) in which the COBE values were so accurate that error bars could be omitted. (When the COBE curve was first displayed to participants at an Astronomy conference, the audience was moved to give a standing ovation; such an extraordinary curve with all points precisely on the best fit version is the dream of all experimental scientists.) When compared with curves determined experimentally for blackbodies of different temperatures, the best fit was to a 2.726° K body; demonstrating that the CBR radiation fits that curve at better than 99% accuracy (an astounding achievement seldom attained in most scientific measurements).
A variant of this includes measurements made by other CMR measuring experiments (different systems). The two plots differ because of different brightness and frequency units and log values are used in the second diagram. COBE allowed the mapping of radiation in the early stages of the Universe, (specifically, at the close of the Radiation Era some 300,000 [perhaps to 500,000] years after the Big Bang, when the plasma in the expanding Universe had cooled sufficiently to become transparent to photons) to an accuracy such that
it showed variations in temperature and density as
slight as 1 part in 10000 during the first billion
years after time zero. Said another way, COBE proved the residual radiation after the Big Bang was smooth to within a fluctuation of 0.01 percent. (Had it been notably rougher, such irregularities would have forced the Universe either to collapse on itself or develop mostly black holes instead of stars.) It also established a range of +/- 30 microKelvins as the range of differences around the average CMR temperature; these irregularities are of the order of 1 part in 100000. The maps below show the broad distribution of these minute temperature differences (ripples) across the early Universe as detected by COBE's DMR (Differential
Microwave Radiometer) using data collected at 53 and
90 GHz. The blues represent slightly cooler and reds
slightly warmer temperatures - thus also define regions
of greater and lesser densities. The top map is the "raw" data plot in which the dipole effect caused by the Doppler motion of the Milky Way galaxy has not been removed. The middle map results when the dipole effect is eliminated, but the radiation from the Milky Way (central band) has not been compensated for. The bottom map is the final product with both dipole and galaxy effects removed - this is the one usually cited as the model for CMB distribution. Another such plot, using different colors, recasts the distribution in terms of the northern and southern hemispheres of the celestial sphere: These small differences were, however, vital in allowing matter to break
from the initial extreme uniformity into regions of slightly cooler, denser
conditions where the protogalaxies could begin to form. Eventually, in the early
Universe these seed fluctuations promoted localized clotting of particles that
became gravitational centers whose growing attraction of more matter led ultimately
to development of the billions of galaxies that populate the Cosmos as we now
know it.
COBE has allowed an estimate of the total energy in the Universe by sampling
yet another part of the spectrum. This results from painstaking analysis of
radiation in the far Infrared using the Diffuse Infrared Background Experiment
instrument onboard. This measures heating of the dust distributed throughout
the Universe, using windows at 140 and 240 µm. However, the overall background
is "contaminated" by dust and other sources within and around the
Milky Way, the Earth's atmosphere, and other sources, which require correction.
The procedure is indicated in this figure:
The upper panel shows a sky map of the Infrared radiation for the whole Universe
with a bright central band representing the Milky Way contribution. The central
projection is the change after Zodiacal light is removed. The bottom panel is
the residual Infrared radiation for the Universe after the Milky Way Galaxy's
influence has been removed. The net effect is that there is much more starlight
in the Universe as "fossil radiation" than heretofore suspected owing
to the masking by dust (ranging from near-Earth to intergalactic) whose influence
is now accounted for with this corrective DIRBE inventory.
In April, 2000 a group of scientists presented the results of project BOOMERANG (acronym for Balloon Observations of Multimetric Extragalactic Radiation and Geophysics) One output was a more detailed map of 3% of the sky which shows variations (with a 35x improvement in resolution) in CBR at the end of the Radiation Era - which also signals the beginning of the Decoupling Era marked by the recombination of protons and electrons to form Hydrogen atoms. This map was constructed by measurements obtained with a passive microwave telescope suspended on a balloon for 11 days at approximately 36400 meters (120,000 ft) above the Earth's atmosphere over the Antarctic. The variations depicted are in units of microKelvins.
Here are several more maps from this experiment using radiation detected at different wavelengths. The upper and lower left maps are at 90 and 150 MHz respectively; the two right maps are differences between 90 - 150 (top) and 150 - 240 (bottom) MHz. The Boomerang scientists envisioned the early Universe to be full of 'sound waves' compressing and rarefying matter and light, producing 'acoustical peaks'. They used this model to calculate the distribution of Dark Matter (30%) and Dark Energy (65%), with the remainder about 4.5% Ordinary Matter, within the components of the physical Universe. COBE and Boomerang results are confirmed, with more detail, by the CBI (Cosmic Background Interferometry) experiment run jointly by CalTech and the NSF. The CBI is located in dry air in Chile's Atacama desert, at an altitude 0f 5080 m (16.700 ft). It started data collection in 1999. Here is an onsite photo of this sensitive instrument:
Thirteen 1 meter diameter dish antennae are synchronized in an array with a broad frequency baseline from 26 to 36 GHz. Each dish receives a different wavelength signal, and interferometry is used to integrate the data from which a power spectrum is produced, as shown by the solid line curve, with values from other CMR instruments also shown:
This next figure is a map of the background radiation over an area equivalent to about 2.2 degrees in declination units (2 widths of a full Moon). The differences being measured are temperature values in microKelvins (µK) that vary around the mean sky temperature of 2.73.. °K. What is being sensed are small temperature differences (range of ~100 µK) when the CBR was around 3000° K. The yellows indicate slightly hotter regions compared with cooler reds and blacks. Associated with these differences are variations in material density - the hotter regions have higher densities, indicating matter has already begun collecting and interacting to generate heat (possible indication that early stars had formed). This observation supports the idea that matter in the Universe at this early time was unevenly distributed, thus pointing to the first stages of (increasing) density/gravity variations required to initiate the process by which galaxic clusters form.
The results from COBE proved of such import to understanding the early
Universe, especially the small but vital fluctuations it detected, that a more sophisticated satellite, WMAP (Wilkinson Microwave Anisotropy Probe), was launched in July of 2001. Background information on this important new astronomical observatory can be found at NASA Goddard's
WMAP site.
The long-awaited preliminary results from MAP were announced at a press conference on February 11, 2003. By then MAP was renamed WMAP, honoring the late David Wilkenson, a leader in the field from Princeton. Cosmologists at this conference stated that the WMAP results were among the most important in the last half century in deciphering the history of the early Universe. The higher resolution of WMAP, in terms of ability to measure even smaller temperature variations, is evident by comparing the new all-skies thermal map from WMAP with the equivalent coverage by COBE: This pair of plots clearly demonstrates the great leap in resolution provided by WMAP, leading to much more detail about the very slight but signficant variations in CBR temperatures. A better view of the distribution of the very small but important blackbody background temperatures is afforded in this projection of WMAP measurements that describe conditions less than a half million years after the Big Bang; three additional spherical maps are needed to cover the entire sky:
Slight differences from the first WMAP shown above appear in the version below (Spring, 2009) which represents five years of data gathering. The variations in color in this, and other maps above, give the impression of notable differences in value. Actually, the temperatures vary by very small amounts. The temperature differences give rise to slight variations in density. But these variations were key to the gradual buildup in differential densities that eventually brought about differences in gravitational attraction leading to local clumping into the first stars and larger scale clumping into the first galaxies. The variations represented by the spread of colors as seen in the WMAP map are an indication of the spatial distribution of the clumps in the early Universe; even though the CBR is now much cooler than in these early times this distribution pattern has persisted. Some very far-reaching conclusions about the Universe have been drawn from interpretations of the WMAP data. One is a new (but still not necessarily the most accurate, although an accuracy of +/- 200 million years is claimed) age for the Universe of 13.7 billion years. The value has superceded the earlier 14.7 billion years that came out of COBE and other studies. This is based mainly on what is believed to be a better estimate of the Hubble Constant: 65 km/s/Mpc. Another WMAP conclusion is strong confirmation of the reality of Inflation during the first fraction of a second after the Big Bang.
WMAP leads also to a better estimate of the amount of detectable Ordinary Matter in the Universe and values for the invisible matter/energy that so far has eluded direct recognition and measurement. These have been reset at 4% for Ordinary Matter, whereas Dark Matter is 23% and Dark Energy 73% (but the results offer no clear indication of the nature of these dark states). (Only a fraction of Ordinary Matter is luminous [gives off detectable visible light], so that the vast bulk of the Universe's constituents is in fact non-luminous and thus hard to detect.) The time when the Universe first became transparent is now given as ~380000 years after the BB. Indirect evidence from WMAP data suggest that massive stars had begun to organize even earlier, perhaps over an interval of about 200,000-300,000 years post-Big Bang. .
COBE and WMAP data have been used to refine many of the fundamental physics and cosmological parameters as shown in this table: However, the list below focuses on what cosmologists consider the 10 most important parameters whose values have been better calculated using the CMR data: The English cosmologist, Dr. Martin Rees has cited his own list of the irreducible number of fundamental parameters that determine the development of the Universe we can measure in his book Just Six Numbers: The Deep Forces that Shape the Universe, 2000, Basic Books. These are: 1) N; = ratio of the electric force holding atoms together to the (much weaker) force of gravity, 1036; if this number were larger then only a miniature and short-lived Universe would have formed; 2) ε = a measure of the strong nuclear force, determined from the energy released in the fusion of Hydrogen to helium (differential of 0.007); if much different than this value, a different mix of chemical elements results, with carbon very scarce; 3) Ω = amount of matter/energy in the Universe (see below); it is the ratio of actual density to the critical density (see below); if too high, the Universe collapses and if too low, expansion would be so fast that there would be insufficient time for stars and galaxies to form; 4) λ = antigravity force (Cosmological Constant); if too large, the Universe would have expanded so rapidly as not to develop as it has; 5) Q = force needed to dissemble a gravitationally stabilized cosmic structure (star; galaxy), measured as the ratio of the energy needed to overcome the gravity force to the energy
bound in the rest mass of the cosmic body, given as 10-5; if Q deviates from this value, a smaller number would have prevented the ripples that gave rise to galaxies, leaving only a dispersed gas but if much larger, only black holes would exist today; 6) D = number of spatial dimensions (3) needed to sustain life in our planet and similar bodies; 2 or 4 would have doomed our existence.
In addition to cosmological parameters, there are also many basic physical constants that are involved in both Cosmology and Physics as practiced on Earth. A discussion of these is given at this
web site. More discussion of many of the parameters, as they bear not only on the origin and development of the Universe but on the appearance of organic life and ultimately Man, is given in the philosophical discussion subsection near the bottom of page 20-10.
The data displayed in the WMAP, CBI and other CMR maps also bear on the model that predicts the Universe had undergone a dramatic Inflation in its initial moments, and in effect provide a positive test of that concept. They likewise point to the notion of a flat Universe that will expand forever (see below). A recent announcement from Hubble scientists carries this cosmic background concept into the visible radiation realm. Based on estimates of quasar populations at
the farthest reaches of observable space (the Deep Field region), extrapolations
of visible light sources to the entire Universe can be made. Results suggest
that most of these sources are now accounted for and that the total amount of
visible light which persists throughout the Universe is approximately of the
order to be expected (by calculation) from the same model that predicts the
amount of Cosmic Background Radiation. In other words, as different parts of
the EM spectrum are analyzed for total energy involved, the numbers remain consistent
with expectations and thus support the energy distribution predicted from the
Big Bang model. The overall notion of an expansion appears on firm ground
based on the ever accumulating scientific evidence. (A CAUTION: A report issued in November, 2003 presents some support for a very KEY topic of controversy in Astrophysics and Cosmology: Have some or even all of the fundamental constants been constant throughout the Universe's history? The speed of light is a leading candidate for dispute and ingenious arguments indicating possible variation. In the report, evidence is cited that the strength of the attraction between nuclear protons and orbiting electrons may have been much greater in the early days of the Universe. The role of quintessence (top of next page) is cited as the factor responsible for this. Other constants are being challenged but until incontrovertible proof is accepted, the "rule of thumb" is to stay with the values (subject to possible minor modifications) cited above.) Some of the recent ideas on the start times for the first stars and galaxies received support and specificity from the WMAP results. The first stars began to form as Supergiants about 200,000,000 million years after the Big Bang. The first galaxies began to organize some three hundred million (300,000,000) years later (possibly earlier). This next diagram depicts these stages (from left to right): 1) initial stages of CBR variations; 2) clots of matter prior to organization as stars; 3) the first supergiants; 4) developing galaxies; 5) galaxies after the first billion years. The time lines for the first stars and galaxies as measured by different space telescopes (JWST is the James Webb Space Telescope planned for 2010; its mission will focus on the early eons of the galaxies, so that the starting time shown above is a "best estimate" for now) are shown in this diagram. Of special import is the new estimate of when the first stars started to form - about 200 million years after the Big Bang. A major future objective of WMAP still to be addressed is to measure extremely small temperature fluctuations that should support/confirm the existence of gravitational waves. These were first postulated by Einstein as a consequence of his General Theory of Relativity. Gravitational waves represent moving disturbances within gravitational fields that are generated by various interactions of matter and/or energy, such as collisions of Black Holes or Neutron stars. With their force particles, the gravitons, they are analogous to electromagnetic waves, with their photons, except that gravitational waves can move unimpeded through matter that itself interacts with photons by absorption.
Like the graviton, gravitational waves have yet to be detected but their behavior and influence within the Universe can be simulated with computer-based models. As gravitational waves move through space, they cause the geometry of space to oscillate (stretching and squeezing it). The wavelength of a gravitational wave depends on the mechanism of its generation.
Theory holds that gravitons and gravitational waves must have first been created during the Inflation period between 10-38 and 10-35 seconds at the outset of the Big Bang. These waves participated in the extreme expansion during those moments and as a result their wavelengths were greatly elongated. The inflationary gravitational waves played a key role in bringing about the slight variations in the distribution of matter and energy during the Radiation Era which ended in the Decoupling Era at which time photons were no longer scattered - this latter period is the earliest in which Cosmic Background Radiation could then be detected. WMAP is seeking to determine more exactly the temperature fluctuations in the CBR field which correspond to the pertubations imposed by the gravitational waves. In theory, these waves are detectable by analysis of the CBR coming from the Cosmic Microwave Background; gravitational waves will cause the radiation to be right or left polarized whereas density variations in the CMB will induce radial polarization (the two modes of polarization must be separated and distinguished by Fourier analysis. The CBR phenomena are proving to be especially fruitful in the study of the Cosmos. It is not surprising then to learn that more satellites are to be put into space to observe the CBR. Next up is Planck, which was launched with its sister satellite Herschel on May 14 of 2009. It will eventually reach its final location at L2, the second Lagrangian point between Earth and the Sun. That location is approximately 1,500,000 km (930,000 miles) from Earth. Planck will have instruments that can measure very small temperature differences using data from 9 different bands. Here is an artist's rendition of Planck. Check out its homepage at this ESA website. In August, 2009 Planck began returning data from which images are made. This example shows the Milky Way (central band) and adjacent areas of the sky (covering a 20° by 20° area) at 9 different microwave wavelengths (LFI refers to Low Frequency Instrument and HFI is the High Frequency Instrument): The first full sky Planck microwave map shows a strip that actually covers 360° but is curved as shown on this projection. The map has been superimposed on a visible light image that highlights the Milky Way (which shows up as the dark red brown patches in the map). The regions off the Milky Way represent temperature differences (as with WMAP, red is warmer than blue) associated with the time of First Light about 300,000 years after the Big Bang. This rendition is not impressive as such, but the image below it shows some details in a 10° by 10° segment of the sky at high latitude off the Milky Way). Eventually, Planck will produce a series of image strips covering the entire sky that will become available (in 2010). The resolution will be superior to that of WMAP. This should aid in improving our understanding of the state of the early Universe.
The modes of behavior of the Universe over time can be classified in several ways: 1) it follows either Newtonian or Relativistic physics; 2) it commenced with or without a Big Bang (i.e, expanding vs steady state); and 3) for the Big Bang case, the growth has been controlled either by Standard Model physics or has been influenced by the Cosmological Constant (or both?).
As a fundamental conclusion drawn from the general acceptance of the Big Bang model for the Universe's origin and development, the initial small space that developed in the first minute has been continuously enlarging - a process analogous to expanding in the manner described on the previous page. However, the precise nature of this expansion, still not fully known, depends on the specific expansion model, as we shall see below. This is related to the amount of mass/energy available to control or influence the expansion. As we will see in the following paragraphs, proposed geometries of the expanding Universe range from spherical to hyperbolic to flat. The duration of expansion ranges from finite to infinite. The terms "open, closed, flat" refer to certain constraints on the curvature of space and on its expansion history. The type of Universe "shape" model - open, closed, flat, spherical - is a factor in the change in the Hubble constant (and the corresponding redshift) with time. A generalized relationship depending on expansion models is shown in this next plot: Before reviewing the various models that were proposed in the 20th Century, we pause to briefly describe a useful and (deceptively) simple view of the Universe embodied in the term Hubble Sphere. This is almost a synonym for "observable Universe" but with one unique property. The sphere moves - it is just that which can be observed at any arbitrary point in the Universe. Earth has its own Hubble Sphere. But a planet in a galaxy 5 billion light years is another arbitrary point and has its own Hubble Sphere. The sphere at each such point has its Hubble Length, which is just the distance outward from the observing point, as an arbitrary center (remember, the Universe actually has no meaningful center), that light has traveled in 1 Hubble time (tH = 1/H). In this framework, that distance is represented as the farthest out that a particular observer at a point can look with the best telescopes to see the first evidence of the Big Bang (which is not really possible owing to the opacity soon after the BB); it is closely related to Lookback time (time for light from an emitter to reach Earth or any other point of reference). Consider the Hubble distance to be the radius r for a sphere that encloses all of the Universe that can presently be seen. That outer limit boundary is, of course, a time horizon and not an actual physical surface encompassing the sphere. As we progress into the future and our instruments "see" still farther, the apparent surface of the sphere moves outward with the increase in rH. There are galaxies beyond the Hubble Sphere; they just haven't been seen yet but will come into view later. Beyond the outermost galaxies, assuming they occur at light year distances equivalent to that of a precisely known Hubble Age, we cannot as of now specify "What's there". Let us now say a few things about the size of the known Universe. It would seem to be determined by the Hubble Distance (DH), which relates to the Hubble Age, around 14 billion years. This is the distance out to the event horizon, the farthest out in spacetime that we can see discrete particles or objects in the Universe. To quantify the distance in Earth kilometers [or miles], just multiply the distance that light travels in 14 billion years by the speed of light. Thus: 14,000,000,000 b.y. x 300 x 104 km/sec x 3600 sec/hour x 24/hrs/day x 365.4 days/year. For this case, the result, which I will call DH, is 1.3245 x 1024 km, or about 1.3245 septillion kilometers.) From the Hubble Sphere model, one might assume that the sphere has a diameter of 2 x DH, particularly when one is aware that the event horizon is essentially the same looking outward, say from the North Pole at the northern celestial sphere and from the South Pole at the southern celestial sphere.
But, this is not so. In relativistic space expansion, the distances outward in opposite directions from the Earth framework are not additive. This is due to the fact that all points in the singularity that are now galaxies were next to each other at the beginning and have simply drawn apart with the expansion of space. With no meaningful center, we can only state for now that space has expanded some finite amount in 13.7 billion years. Euclidian size is not a valid way to look at the Universe, whatever "shape" it may have, as implied from the paragraphs later on this page. In trying to think about "size" there is a further complication. The expansion during the Inflation period (see page 20-1) may have proceeded at rates faster than the speed of light. If so, the Universe may really be much bigger than what we deduce from event horizon distances. We get our idea of distances only from measurements of z and H as determined from we see now in the Universe after the galaxies formed. Prior to those times, inflation expansion, yielding much greater z and H values, could have pushed the outer edge of the Universe to distances well beyond what can be detected as apparent event horizons. One interesting corollary to this reasoning is that in principle cosmologists can detect galaxies that appear to be receding as speeds that when calculated seem to be exceeding the speed of light. This is because the Hubble constant isn't constant, it is increasing. This apparent contradiction to Einstein's relativity demand that light has one fixed finite value is explained on pages 40 and 42 of the previously cited Misconceptions about the Big Bang, by C.H. Lineweaver and T.M. Davis, Scientific American, March 2005. So, what can we say about our understanding of the size of the (our) Universe. Its minimum size must be at least as far out in spacetime as we can see galaxies, quasars, and supernovae - 14+ billion light years to the currently known event horizon. We cannot [yet] see timewise to anything before the Radiation Era; Cosmic Background Radiation, which traces to about 300,000 years, is pervasive and thus not location-specific. The maximum conceivable size is infinity, with "outer limits" reachable only in infinite time. If the Universe is indeed infinite, its present outer limits are not fixed in any way, as they will enlarge forever in their expansion towards infinity. If the Universe is proved to be finite (possibly contrary to the most likely scenario - see below), then its boundary is almost certainly beyond the event horizon we now see - there are more galaxies farther away which will become visible as time progresses and DH lengthens. The safest conclusion now reached under currently postulated scenarios is just that the Universe must be larger than the presently determined horizon distance. But thoughts on size are changing. We can set a lower limit of the observable Universe at the currently most favored age of 13.7 billion years, that is, we can now see out to that part of the outer Universe that contains all the stars within a "sphere" in which light has traveled no longer than 13.7 billion years at its present speed. And we see that value in any direction we look. Perhaps this means that we are near the center of a finite Universe. If so, its diameter would about 29.4 billion years. But when the fact that the Universe is now accelerating (as discussed on the next two pages), this must be taken into account.
Dr. Neil Comish and colleagues at Montana State University have done a preliminary calculation on how much the Universe has expanded since the first radiation around 13+ billion years was released and is now just being received on Earth. But because the Universe has expanded tremendously since the Big Bang, the distance that light has been traveling continues to increase during the 13+ billion year timeframe. The source of the primordial light leaving the very early Universe from any point (say, the first star), has thus itself moved much farther than the time-travel distance. Their model leads to an astounding number - 78 billion light years to the edge of today's Universe and a possible diameter of a spherical Universe of 156 billion l.y. (so large both because of the effects of spatial expansion and acceleration rates since about 6 billion years ago. One might conclude that this requires different values for the speed of light in the past, which might seem to violate the General and Special Laws of Relativity, but the astronomers point out that this speed remains constant while the distance a photon released at the beginning of the Universe must travel is what is increasing. This estimated diameter and other figures for size are obviously still controversial but the "true" size should be increasingly refined in coming years. A summation: Lets say that we detect a galaxy that is 13.5 billion light years away. It has taken that long for light near the dawn of cosmic time to reach Earth. Is that the size of the Universe? An emphatic NO! It must be larger. At the time of light departure, the actual Universe THEN was much smaller - about a 1000 times less than at present. Over the 13.5 b.y. travel time, the Universe has expanded (not at a uniform rate but with the decreasing acceleration in its first half of existence and now replaced by an increasing acceleration, as described on the next page). The important point is that growth of the Universe during the 13.5 b.y. time of travel has stretched out the actual size even as the light had to continue to make its way to Earth observers. The fact that this burst of light 13.5 b.y. ago ultimately reaches us happens because the total growth rate is notably less than the speed of light. Relativity is built into this description (consider the analogy of one walking from one end of a train to the other even as the train moves along track; the total distance traveled is some combination of person walk plus train progress). Hopefully, this paragraph may clear up any uncertainties you retain after working through other relevant parts of this Section. But, if you would like more information on the size and shape of the Universe, consult this Wikipedia website that discusses the Observable Universe.
Relativity has played a vital part in the models of the Universe that remain the most plausible. The expansion of the Universe (in terms of rate of change of the Scale Factor R = r/r0) from a relativistic framework can be summarized as the
Friedmann equation. For the distribution of matter in the Hubble sphere, the equation considers the contributions of both the gravitational potential energy and the kinetic energy of expansion. We give it here in two forms, the first as a differential
equation:Cosmic Ages: The Age of the Universe
t0 = 1/H0.
Age t0 (years) = 979.3 x 109/H0
Cosmic Background Radiation
Evidence for the Expanding Universe
Major Models for the Spacetime Universe:
And the second (introducing H):
In these equations, Π (pi) is the familiar constant (ratio of a circle's circumference to its diameter = 3.14159...), G is the Universal
Gravitational constant (6.6726 x 10-11 m3/kg/sec2), ρ is a Greek letter denoting the average density of
the Universe, k is a curvature constant in which values of 0, +1, -1 represent
flat, spherical, and hyperbolic geometries respectively, R is the Scale Factor
for the observable Universe, H is the Hubble Constant, c is the speed of
light, and t is time. A solution to the Friedmann equation depends on which Universe model
is being tested, as the group described next has different values for key parameters.
Several cosmological scenarios, named after the scientist(s) who first proposed
each (several scientists came up with more than one model), for various modes
of expansion lead to different end results (shown graphically below for four general
models).
In common, they all obey the Cosmological Principle, which states that the
Universe is both homogeneous(defined as being the same at any point within space) and isotropic (as one looks out, appearing the same in any direction. This boils down to having essentially the same
average distribution of matter/energy in all directions) on the largest
scales (500,000 light years and larger. This is not violated at the scale of galaxy clustering since at the
universal scale these tend to be "smoothed out" by having much the
same patterns anywhere one looks. Open models also must be consistent with
the restriction placed by the Second Law of Thermodynamics which from a cosmological
standpoint states that over time the entropy (a measure of disorder of
a system) must ultimately increase to (or towards) a maximum (total disorder). Interpreted at a universal scale this would lead to complete dispersal of galaxies
and their stars (perhaps rearranged as randomly distributed Black Holes) and
blackbody temperatures approaching zero. A corollary holds the initial singularity
to have minimum entropy which then rapidly increases during the first moments
of the Big Bang. Note that when the above curves are extrapolated back in time, they strike the horizontal
axis at different positions (times). This means that the age of the Universe will vary relative to
the particular model being considered. Thus, although the current Hubble time (1/H0), which depends
on the accurate determination of the rate of expansion, leads to an age or duration of the
Universe, that value can be modified when (and if) a particular expansion model is shown to
be the best or valid one.
The following table (modified from Hawley and Holcomb, 1998) summarizes the principal Cosmological Models that have been
developed and tested by calculations. They fall into two groups: Non-Big Bang and Big Bang. Another distinction category: Models in which the Cosmological Constant L (see below) is a factor (upper five rows of table)
and the Standard Friedmann (or Friedmann-LeMaitre) models in which L is not involved (i.e., is O; bottom three rows); the three standard models also have Deceleration
Parameters q (defined below) that include the value 1/2 in some way.
|
|
|
|
|
|
| de Sitter | Flat (0) | >0 | -1 | No BB; exponential expansion; empty |
| Steady State | Flat (0) | >0 | -1 | No BB; uniform expansion |
| Einstein | Spherical (+1) | Lc | 0 | Static; H = 0; now, gravity balanced by repulsive force; may be unstable |
| Lemaitre | Spherical (+1) | >Lc | <0 | Expand; hover; expand |
| Negative L | Any | <0 | >0 | Big Crunch |
| Closed | Spherical (+1) | 0 | >½ | Big Crunch |
| Einstein-de Sitter | Flat (0) | 0 | ½ | Expands forever; density at critical value |
| Open | Hyperbolic (-1) | 0 | 0<q<½ | Expands forever |
q = The Deceleration Parameter: denotes the rate of change with time of the Hubble Constant and R; a positive value indicates acceleration; negative = deceleration.
L = The Cosmological Constant, introduced by Einstein to his
field equations for General Relativity in order to provide some constraint
to gravity (a counter-effect) to avoid an inevitable collapse of the Universe;
if + (repulsive) L counteracts gravity; if - (attractive) L may
be equivalent to the vacuum energy density associated with particles at the
quantum level. (L in texts is also given by a capital Greek letter Λ). The current value for energy density within the observable Universe is between 1 and 5 x 10-26 kilograms per cubic meter.
The Steady State, de Sitter, and Einstein Universes, all non-standard, are currently not supported by observational evidence. The more general diagram above showing four alternative expansion models can now be redisplayed in terms of the names associated with some of the specific models described in the above table: From J. Silk, The Big Bang, 2nd Ed., © 1989. Reproduced by
permission of W.H. Freeman Co., New York The nature and shape of the Universe depends on its mass density (including energy forms that relate to mass according to the E = mc2 equivalency).
The key parameter is the Critical Density, symbolized as ρcrit, and is calculated as ρcrit = 3H2/8πG. ρcrit is derived from the Friedmann equation; conceptually, it is the amount of matter/energy needed to lead to flat spacetime, in which the Universe is neither open or closed. Using the current value of H as 22 km/sec/Mly, ρcrit is 9.7 x 10-27 kg/m3. Since Hydrogen is by far the most abundant element in the Universe, ρcrit can be presented as an average of 5.8 atoms of H per cubic meter. ρcrit is postulated to be just that total mass/energy that causes the Universe neither to expand forever nor to collapse on itself, i.e., it is flat and will just stop expansion after infinite cosmic time has elapsed. Thus, a flat Universe is one that expands at the "balanced rate" that permits it to just avoid an eventual collapse.
Ω is a fundamental parameter that is the ratio of the actual density to the critical density. In terms of the Friedmann equation, Ω = ρ/ρcrit = 1 + kc2/H2R2; k is a measure of curvature and R is the radius of a Universe considered to be spherical . Ω values have been determined for all the prime constituents of the Universe and have these (approximate values). Ωde (dark energy) = 0. 73; Ωdm (dark matter) = 0.23; Ωat (atomic matter) = 0.044; Ωph (photons) = 5 x 10-5; Ωnu (neutrinos) = 3.4 x 10-5. These will sum to Ωtot (total) = 1. In the more general case, Ω is often expressed as ΩΛ for all Dark Energy and ΩM for all matter, both Dark and Ordinary. In the more general case, Ω is often expressed as ΩΛ for all Dark Energy and ΩM for all matter, both Dark and Ordinary. The history of ΩΛ and ΩM over cosmic time has been one of progressive increase of the first at the expense of the second. Thus, ΩM was nearly one (1) at the beginning of the Universe and now has diminished to 0.27 (0.23 for Dark Matter and 0.04 for Ordinary Matter) will continue to decrease in the future as ΩΛ increases beyond the present 0.73, causing ever increasing expansion. As a practical measure it is estimated that, if all atomic matter - both galactic and intergalactic - is redistributed to spread uniformly through space, its mass density will average just under 6 atoms per cubic meter. This is notably lower in the parts of space far from galaxies. This near vacuum space will contain mostly Hydrogen atoms. The least populated parts of intergalactic space are "almost totally empty", not quite a true void having about 1 atom per cubic meter, but consists of Hydrogen atoms, traces of other atomic species, ions, infinitesimal amounts of ice and dust (including possible organics), virtual particles and Dark Matter/Energy - all in very low amounts. The intergalactic density distribution also likely varies, becoming higher as galaxies are approached. Individual stars and nebular clouds are found in parts of intergalactic space as local regions of concentrated matter.
There are three general density-controlled shapes available as options for the configuration and expansion of the Universe. Their geometric characteristics are depicted in this next figure. Note that two properties help to define the nature and behavior of each shape: 1) What happens to so-called parallel lines in traversing the shape, and 2) What is the sum of angles in any triangle drawn on the shape?
The spherical shape is said to have no boundary in that one would always remain on its surface and if "walking" along a great circle would always return to the starting point. It has positive curvature. Hyperbolic space is one that has negative curvature: although difficult to visualize, and best described mathematically, descriptively it has been likened to a horse's saddle; this geometry has the peculiar spatial attribute that movement away from the lowest point on it can go either "downhill" or "uphill", depending on direction. Flat space has minimal (zero) curvature and obeys the precepts of Euclidean geometry. Spherical, flat, and hyperbolic space have this defining property in which the sum of the angles in a triangle are greater than, equal to, or less than 180° respectively. In flat space, parallel lines remain parallel in this geometric sense; this provides a means to test the type of Universe geometry that corresponds to reality. This implies that light beams from a distant source do not converge or diverge. So far, evidence is that lines of radiation travelling in space remain parallel unless disturbed by gravity from massive bodies. Both flat and hyperbolic space can extend indefinitely (to infinity) in contrast to spherical space (but, in principle, if it expands continuously forever that too could lead to a kind of infinity).
These three general types of shape can also be depicted in spacetime cone figures, such as this one, showing from left to right the steady, decelerating, and accelerating expansion models:
From the above, one theoretical way to distinguish which shape best describes that of the Universe: send two light beams oriented parallel to each other but separated by some distance. In the flat Universe, these beams will always remain parallel. In the hyperbolic Universe, the beams diverge; in the spherical Universe they will eventually converge and cross each other. (Theoretically, the test could be compromised by the beam being affected by strong gravitational forces, as has been demonstrated for predictions made by Einstein's General Relativity.)
If the the total density (choosing M as the sum of all matter and all energy; remember that energy can be stated in terms of mass by Einstein's famed equation, restated: m = E/c2) distributed throughout a finite Universe of some size or volume V is less than the Critical Density, space is hyperbolic and open; if greater than critical,
spherical and closed; and if equal to critical, space is flat (at least at
the scales we observe it). This can also be expressed as the Density Parameter or Ω which is the ratio of the actual densities ρ of matter and energy present in the Universe to ρc, the density that would apply to a Flat Universe expanding to infinity. The Open, Flat, and Closed Universes are associated with Ω > 1, = 1, and < 1 respectively.
Each of those models fits at least some of the general observations
of the Universe but has failed on other accounts. Considering all of these models: If the Universe is open or
flat, the Universe will expand infinitely but at different rates depending
on the parameters associated with each model. The closed and negative L models,
in contrast, predict finite expansion followed by eventual contraction and
thus at some time the Universe returns to a singularity state. For each of
the models, the expansion geometry and the behavior from the onset (the Steady
State model has no "beginning") to its eventual fate (Crunch; Expansion)
depends ultimately on the matter density that characterizes it. As stated earlier on this page, the presently favored model for the Universe's geometry is "flat" (although an Ωtot of 1.02 [see table above] suggests it may be slightly open). This seemingly contradicts the notion of expansion of a sphere. But when the size of the sphere is huge (radius estimates vary but can be greater than 42 billion light years), if one is located at any point "on" the sphere, the curvature is so slight that the "surface" appears flat. The relevance of "flat" is that it describes a geometry that is Euclidean. The first five models are all non-standard and were devised
when Einstein's Cosmological Constant seemed to have some essential validity.
He introduced Λ to his field equation that described the Universe's status in terms of the Friedman model (see above), yielding this equation:
This is an appropriate point at which to elucidate this famed Cosmological Constant. Einstein himself spent many years in calculating properties of various Universes. Einstein favored a static Universe (neither expanding nor contracting). But gravity should cause the Universe to eventually collapse. To offset that effect, Einstein postulated a form of vacuum energy density that would be positive in the sense of countering gravity (in a sense, causing offsetting expansion that just balanced to contraction from gravity). This he named the Cosmological Constant. It is usually represented by the Greek letter Λ and is expressed in this equation, in which ρ is the density term, G is the Universal Gravitational Constant, and c is the speed of light:
When Hubble and others presented ever more convincing evidence that the Universe was actually expanding, Einstein refuted his Cosmological Constant, calling it the "greatest blunder of my life".
In recent years variations of the Cosmological Constant are again becoming fashionable to explain some of the phenomena essential to a changing Universe, as we shall see on the next page which dwells upon an Accerating Universe. Its possible
equivalence to the concept of u>vacuum energy density that may be the nature of Dark Energy (next page) has rehabilitated the idea. It may also have been a key factor
in the Inflationary Stage of the early Universe; a rapid increase in L (the
Lambda-force) could be the driver behind the tremendous expansion then but
that increase had to be short-lived and L must revert towards zero or the
Universe would have long since "blown" away.
Values for Λ are hard to come by even in modern textbooks. The current values are associated with vacuum energy density. The ones quoted in the Wikipedia web site on the Constant are "on the order of 10-35 s-2, or 10-47 GeV, or 10-29 g/cm3,[5] or about 10-120 in reduced Planck units."
The Einstein Universe is a static one, with spherical geometry. It was put forth by this great scientist as an attempt to apply General Relativity
to Cosmology. The idea of the Big Bang had not yet captured the attention
of cosmo-scientists. In order to keep the Universe "going" instead
of collapsing under its own gravity, Einstein invented his Cosmological Constant L to balance
the attractive forces. While now considered notably incorrect, this type of Steady State model
stimulated others to propose variants that incorporate expansion. The de Sitter
Universe is a strange one, being empty and never undergoing a Big Bang. Its
value of q being negative (-q) denotes an accelerating Universe. But in working
back towards time zero, its representative R(t) value never attains zero,
which means that it has no beginning, i.e., has an infinite past. While theoretically
interesting, the model defies most observational parameters, and the very notion of the Big Bang concept. The Steady State
Universe was formulated by Hoyle and others as an "antidote" to
the Big Bang model. It accepts expansion and implies that the Universe has
no beginning or end. In order to preserve the matter density distribution
determined for the Universe, the Steady State model requires a "creation field"
in which new matter (mass) must be continuously created through time to balance
the rate of expansion. Another model (not in above Table) also does not start
with a Big Bang; this, the Eddington-Lemaitre model, is closed and finite
and is static initially but thereafter starts expanding when the galaxies
begin to form by Hydrogen gas condensation.
The Lemaitre model, derived from
the Big Bang concepts, begins with a rapid increase in R during the early
Universe but then experiences an extended period when R(t) remains nearly
constant (owing to the effect of L being greater than Lc) so that
expansion is minimal ("hovers") until much later resuming at an
accelerated rate (read the modern version of this resumption of acceleration on the next page). The Abbe George Lemaitre (a Catholic priest from Belgium who also was a physicist) was the first to consider the starting state to
be one of extremely high (approaching infinity) density (he called the singularity
a "primeval atom"; later, George Gamow applied the Greek word "ylem" [primitive
matter] to everything contained in such a singularity).
Among the three standard hot (high temperature) Big Bang models,
the Open Universe model (also known as the Friedmann-Lemaitre model)
predicts that expansion continues forever at an essentially constant rate
through an infinite and unbounded space based on hyperbolic geometry (in which
light can follow both positive and negative curvature simultaneously). Evidence
so far suggests that a (nearly) flat Universe model, whose density
is at the critical density (in which Ω = 1, the condition that there is just enough matter distributed throughout the Universe to cause it to expand forever even as it endlessly slows down)
accounts for many of its observed properties, so that the Einstein-DeSitter
Universe is currently the model most widely held to approximate reality. This model is in accord with current estimates for the age of the Universe.
The mental picture one gets from the word "Flat" as we have been applying it to cosmic expansion may be somewhat illusory. One meaning - just as the surface of a large balloon may
appear flat to an ant at some point on it, so the Universe may in fact be
spherical but acts as though flat within the region open to our direct observation (we experience this on Earth as our local surroundings appear flat out to the horizon but would show its real curvature if we were orbiting astronauts). However, flat on a Universe scale may mean just that - flat in our experiential Euclidian sense - imagine a table top that keeps expanding forever from within itself (not just by growth at the edges) in two primary directions; points at different parts of this infinitely growing top would all separate from each other. Table tops do have a third dimension (thickness), as presumably does a flat Universe, but expansion in that dimension may be finite.
Closed Universes follow spherical geometries. The prime
model shows greater rates of expansion in early cosmic time with decreasing rates of augmentation
thereafter. (This is not the same as
the incredible but brief expansion almost at the very beginning of the Universe
if inflation indeed is a real phenomenon.) Thus, the components of the Universe move outward powered in part by the inertia imparted by the energy release at the Big Bang. However, the mass/energy level is high enough for gravity to effectively pull on galaxies, stars, and other matter so as to gradually slow the expansion to a zero rate. Thereafter, the condition becomes one of increasing deceleration. The rate of separation between galaxies diminishes with time until,
at some future time, expansion ceases and galaxies then draw closer at ever
faster rates until all matter and radiation converge to a singularity (perhaps
50 b.y. in the future), undergoing what has been called the Big Crunch.
The Crunch concept remains intriguing. A group at Penn State University has carried out computer calculations that strive to combine General Relativity and Quantum Physics to derive a Quantum Gravitational model of a contracting Universe. This results in matter and energy in that previous Universe coming together in the singularity we know as the Big Bang. As contraction proceeds to its last moments, at its terminal stage quantum forces become repulsive, causing a quantum Big Bounce that seems similar in its properties to a Big Bang. Their model retains a consistency that does not rule out this possibility but the difficulty of trying to find confirmative evidence for this earlier Universe is only addressed in terms of the model being plausible without any direct proof. This raises the possibility of Repeated Universes, as singularities
explode, expand, ultimately contract to the next singularity, and then repeat
the cycle indefinitely, or, even infinitely. However, this scenario seemingly
would violate the entropy restriction in that the singularity should have
a minimum rather than maximum state of disorder that is the outcome for every
model. Multiple Universes (next page) that evolve simultaneously, or at different "times", are a possible consequence
of the Chaotic Inflationary model which in recent years has gained
favor as a variant of the inflationary version of the Big Bang. These Universes,
however, have no likelihood of contact with one another, so that their existences
may be unprovable.
To sum up this topic - the shape of the Universe. Evidence is building that the Flat condition is the most likely to describe this configuration. However, this "flatness" may be illusory: the Universe may be so large that what is viewed and perceived as "flat" is actually part of curved space - as viewed the curvature is too slight to be determined (imagine being on a small part of a very large balloon). Results from COBE and WMAP seem to offer solid support for the idea of real or apparent "flatness". Consider this diagram: The closest fit of size variations of cosmic background radiation fluctuations, as determined by calculations, to the observed COBE and WMAP data is that of a Flat Universe. Nevertheless, whether the present Universe is open, closed or flat is still being debated, despite the ever-stronger support for a Flat Universe. The key factor is the mass density of the Universe. If this amount
lies below a precise value, then gravitational forces will be insufficient
to finally halt the expansion that would eventually result in all matter throughout
space being pulled back into closure; in the open case, expansion is forever
in (apparently) the one and only Universe. As of now, inventories of mass
within the Universe have come up way short of the amount actually identified as to their nature needed to maintain a closed Universe but with further observation and experimentation the gap is narrowing. If the interpretation of WMAP data is essentially "on target", then the condition that the total Universe mass is close to the Critical Mass allows for a fairly precise estimate of how much mass must be found and accounted for.
The bulk of the missing mass (and energy particles that have mass) is believed to exist as Dark (non-luminous, i.e., does not give off [detectable] electromagnetic radiation) Matter of still uncertain types and/or as neutrinos, and thus remains at present "invisible" to astronomers' detectors. Theory presently holds that most proposed kinds of Dark Matter do not interact with baryonic (Ordinary) Matter, although some Dark Matter may be baryonic. Dark Matter is currently difficult to detect and thus its amount is hard to quantify. Dark Energy, a closely related topic, is mentioned briefly in this subsection but will be examined in some detail on the next page. Suffice for now to state that the main role of Dark Energy seems to be that it has some property the counteracts the effect of gravity in slowing down or decelerating the Universe's expansion. Dark Energy thus produces an accelerating force which is the best current explanation for the recent observation that the Universe is now expanding or speeding uup(and appears to have resumed a net expansion in the last few billion years).
Some of the Dark Matter seems to associate with the galaxies. Theory says that Dark Matter plays a key role in galactic development and stability. The galaxies themselves contain insufficient mass to provide the gravitational strength needed to hold them together. Since they are intact, it is a logical inference to assume the existence of Dark Matter which supplies the gravitational forces that maintain them. A computer simulation reported in late 2003 indicates the bulk of Dark Matter occurs in large "clumps" distributed throughout intergalactic space; see further discussion below. Black holes may serve as collectors or maintainers of this Dark Matter. A recent estimate states outright that Dark Matter and Dark Energy together comprise ~95% of the Universe's mass (remember Einstein's mass-energy equivalency), with varieties of normal or baryonic matter accounting for the remainder are thus less than 5%. This means that most of the matter in the Universe presently is invisible to detection from Earth (the billions of luminous galaxies, each with billions of stars therefore make up only a tiny fraction of the Universe's total mass).
This humongous amount of Dark Matter is postulated by inferences
drawn from observed effects; indirect evidence comes from the behavior of
galaxies and galactic clusters which seem to need this superabundance of mass
to account for their stabilities and motions. For example, the velocities
of stars in outer galactic spiral arms is much greater than predicted from the Newtonian
1/r2 force law, implying excess external mass. Thus a sheath of invisible Dark Matter/Energy acts to prevent galaxies of spinning apart by holding the fast-moving outer stars in a gravitational bind.
Another line of
evidence comes from the gravitational lens effect (see text and illustrations in the Preface page of this Section) - much more mass than observable
is needed to account for the degree of bending of space as predicted by General
Relativity. This is revealed by a greater curving of light from more distant
light sources (therefore displaying larger displacements than expected) than
would be caused only by the mass of the specific galactic cluster whose gravitational
influence is being tested. Another sign of concentrations of hidden mass relates
to directional movement of galaxies near enough to observe and measure this
motion. Close to home, our Local Group (including the Milky Way) of galaxies
is moving through space in the direction of the Constellation Centaurus at
greater than expected velocities, under the influence of an invisible mass
concentration dubbed "The Great Attractor."(by itself, the Milky
Way is moving at about 2.1 million km/hr towards the region around the Constellation
Leo). Also, huge masses of glowing gas whose molecules are rapidly moving
and hence indicate very high temperatures have been detected; being very hot,
they should fly apart but clearly are holding together, indicating the attractive
action of great quantities of invisible mass.
There is evidence that older, more primitive stars (that have a paucity of those heavier elements that were produced in stars and dispersed by supernova explosions) contain around them higher concentrations of Dark Matter. But, much (most?) of the missing mass may be tied up in Black Holes; billions
probably exist throughout the Universe, and many, if not most, of the galaxies
have Black Holes in their central cores. A Black Hole with immense mass has been verified
at the center of the Milky Way, around which the inner stars revolve about
the Hole at speeds up to 3 million km/hr as they spiral inward to eventually
be sucked in (by comparison, the Sun orbits around the galactic center at
~790,000 km/hr and the Earth around the Sun at ~108,000 km/hr).
The composition of Dark Matter is still speculative. Candidates are shown in these diagrams, modified from that which appears in the page dealing with the nature of the Dark Universe found on the University of Oregon Astronomy site we have referenced several times in this Section:
Some of the baryonic Dark Matter occurs in what is
called MACHOs (for MAssively Compact Halo Objects), consisting of baryons
(protons, neutrons) and other matter (probably some fraction of the neutrinos pervading space) in the non-radiating dark halos now known
to distribute around galaxies and in intergalactic space (see below). In the halos they constitute most of the faster moving Hot Dark Matter (HDM). MACHOs contain enough extra mass to provide the gravitational boost that holds galaxies together (motion in the spiral disk would otherwise cause a galaxy to fly apart). Dwarf galaxies and Wwhite
and Black Dwarf stellar remnants - too small for ready detection in more distant
space - may also abound in this material. Black Holes, Neutron stars, and Dwarfs, undetectable
by visual means but identified by their gravitational effects on nearby visible
stars, also make major contributions. In fact, the same (as yet undetected) material as occurs in MACHO's may also make up planet-sized Black Holes, whose numbers in the Universe can be huge; this is not yet verifiable if a B.H. is "standing alone", i.e., does not have a companion star(s) feeding it material that becomes excited and luminous.
One MACHO type is the neutrino whose existence
has now been proved. Once thought to be massless, a tiny but real neutrino mass has only recently been verified - a determination that could account for much (most?) of the "missing"
Universe mass. Neutrinos (electrically neutral) are found not only in haloes but appear to pervade the "empty space" of the Universe. An announcement in June 1998 by a Japanese-American research
team may dramatically change the role of neutrinos in the mass balance sheet.
Using a deeply buried detector and a huge array of detectors, they have been
able to capture light signals set off by neutrinos that disclose these extremely
small particles to have an infinitesimally minute mass, about one ten-millionth
that of the electron. But, because of the extremely large population of neutrinos
throughout the Universe (like the Cosmic Background Radiation, they too are
a residue of the Big Bang, being especially produced in abundance during the
first few minutes when protons were being fused into Deuterium and Helium nucleii
releasing energy as neutrinos), the cumulative mass of these particles may
make a sizeable contribution to the inventory of missing mass. But other
theoretic MACHO(s) that remain to be discovered (either from future
particle accelerator experiments or from still-to-be-built, more sensitive
space detectors) will likely constitute the bulk of the MACHO population. Concerning neutrinos as a component of Dark Matter, until recently there was still considerable uncertainty as to whether neutrinos (there are several varieties) have any mass at all. They rarely interact with matter and are thus very hard to detect. At this instant, billions of neutrinos are passing through your body, and perhaps one or two at most will meet with an atom. Experiments in several countries are attempting to find out more aboutthe elusive neutrino. Below is one example of an experimental detection setup. Several thousand feet below the surface, in a large alcove in a nickel mine near Sudbury, Ontario (the overlying rock screens out most other high energy particles that might produce false signals), is a 12 meter diameter sphere containing heavy water (deuterium instead of Hydrogen). Around it are a bevy of event detectors. A few events have been ascertained, but the number of solar neutrinos appears lower than theory had predicted.
If the neutrinos are finally assigned a specific (but tiny) mass, they must be a major component of Dark Matter. The estimated ratio of Dark Matter neutrinos to Ordinary Matter neutrinos is 100,000,000 to 1. A significant fraction (perhaps the bulk) of the missing matter, however, seems to occur in Cold Dark
Matter (CDM), probably in the form of slow-moving WIMPs (Weakly Interacting
Massive Particles) - elusive matter/energy that does not interact with electromagnetic (EM) or strong nuclear forces. These appear to be heavy nonbaryonic particles (50 to 100 times the mass of a proton) of still unknown nature. They may also include two specific particles that have been postulated but not yet found experimentally: the neutralinos and the axions - both predicted to exist according to SuperSymmetry theory. Several high energy accelerators are either now operational or are being built (the best and biggest is CERN's Large Hadron Collider [LHC] in Switzerland) to find direct evidence of the existence of WIMPs or some similar form of matter.
Recent reports from several investigator teams claim that much of the Dark Matter is accounted for by the very hot gases that are believed to pervade the intergalactic space that appears "empty" compared with galaxies and nebular clusters of visible gases. A clue to the presence of these gases (undetected at Visible and longer wavelengths) was found in UV spectrum data but the signal was weak. However, when Chandra data for X-ray radiation was collected from intergalactic regions, indications were for very hot gases in signficant concentrations in the so-called void. An estimate of gas densities was obtained by calculating the weakening of certain wavelengths as radiation from a gas-rich region passes through a nebular mass. This is shown diagramatically: The relative amounts of Dark Matter and Dark Energy have been calculated based on data collected in the past few years. This is conveniently displayed in this pie-chart diagram, made in the mid-1990s, that includes all physical entities:
In this diagram, Ordinary (detectable) "Matter", mainly in the star-studded galaxies, amounts to only 0.5%. Photon radiation moving about the Universe contributes just 0.005%. The MACHOS make up the Ordinary (including nonluminous) Matter (4%) and WIMPS comprise the Exotic Dark Matter (25%). The bulk of the ingredients in the Universe is what is known as "Dark Energy", and accounts for ~70% of the estimated total mass/energy; conjectures as to its nature are described on the next page in the paragraphs that deal with the repulsive energy that could relate to Einstein's Cosmological Constant.
The WMAP data have resulted in a further refinement in the percentages of Dark Matter and Dark Energy. This diagram shows a shift to a 3% larger amount of Dark Energy with a 2% decrease in Dark Matter: In February 2003, F. Nicastro and his associates at the Center for Astrophysics of Harvard's Smithsonian Astronomical Observatory reported a more precise calculation of the numbers for Ordinary Matter. Of the 4% that comprises the total amount, about 0.4% is luminous (in the visible range) as the stars making up galaxies. The remainder consists of H, He, and other Baryons that occupy both galactic halos and beyond in intergalactic space. These exist in a high temperature (105 to 107 degrees Kelvin) "fog" that they have detected using both FUSE (Far Ultraviolet Spectrometer Explorer) and Chandra (X-ray) data. This fog is left over from the galactic formation process and serves to provide the extra mass needed to gravitationally bind together galactic groups (they studied the Local Group around the Milky Way) in clusters. The roles of Dark Matter and Dark Energy in the observed Universe are still being worked out. Both, or perhaps Dark Matter in particular, seem to be needed to keep the galaxies intact and to prevent them from collapsing into each other. It appears that the gravitational forces from the matter within a galaxy are insufficient to keep them from flying apart and dissipating into intergalactic space. Dark Matter should provide the mass needed to furnish the gravitational stability that maintains the integrity of the galaxies once formed. In fact, several models for its existence and nature consider the bulk of Dark Matter to occupy large invisible halos surrounding the galaxies, serving as the major gravitational "glue" that holds them together. And, as will be discussed on the next page, Dark Energy, as inferred by theorists, is a positive force that is responsible for the increasing expansion of the Universe (thus, it counteracts gravity) An imaginative explanation for why Dark Matter (in terms of mass) has so far eluded scientists as to proving its existence and nature has been proffered by Dr. Jonathan Feng and his group at the Univesity of California-Irvine. They postulate this matter to be hidden particles that reside in an extra dimension beyond the three spatial ones that we sense. This is plausible if the multi-dimensional space described at the bottom of page 20-1 is a reality. This model may be provable by this means: the extra-dimensional mass particles would tend to collect around bodies that have strong gravitational pulls. Under this influence, the particles would tend to collide with each other more often, producing neutrinos with especially high energy. Experiments to test this hypothesis have been proposed. One test for the existence of Dark Matter (and probably also Dark Energy) is that of the (Einstein) gravitational lensing effect (bending of light as it passes by a massive galaxy). If only the luminous matter in the galaxy, supplemented by assumed mass in contained black holes, is operative, the amount of deflection should be less than observed. In fact, that deflection is greater than this simpler case, and thus has been attributed to at least MACHOS and/or some amount of WIMPS that are emplaced in and around the galaxy. Using gravitational lensing techniques, the size of the Dark Matter distribution concentrated around galaxies has been estimated to be in a roughly spherical arrangement (the 'halo') up to about 5 times the radius of each galaxy examined so far. Gravitational lensing has been used to create this image of a group of galaxies, in which the pinkish halo around each is the estimate of the size and position of Dark Matter holding each intact: Incontrovertible proof that Dark Matter and Dark Energy really exist, and insights into their nature, rank near the top of priorities that astronomers and cosmologists intend to address in the first decade of the 21st Century. A number of approaches besides gravitational lensing have been proposed. One is to compare the size of a galaxy as seen in visible light to the size of its associated hot matter (the "fog") that gives off strong X-ray radiation. Look at this pair of images of a galaxy in the Virgo galactic cluster:
Another, oft-cited, example of the X-ray envelope is the NGC 2300 galaxy group, consisting of a number of individual galaxies as seen in Visble light that do not show up as individuals when X-radiation (measured by ROSAT) is assigned colors to indicate its extent. How do these X-ray images indicate the presence (existence) of Dark Matter? The argument is that the galaxies would have flown apart by now but are held together by the mass associated with the Dark Matter that encloses them. Consult the University of Oregon page cited above for illustrations that define this process. A variant to the size argument is to study the shapes of galaxies that have characteristics explainable by the presence of Dark Matter. MGC 720, some 80 million light years away, shows differences between Visible and X-ray images that can be postulated as imposed by Dark Matter in the halo surrounding the galaxy. As seen below, the galaxy has a flattened elliptical shape when viewed in Visible light but as imaged by the Chandra X-ray Telescope the core appears round and the surrounding excited matter is distributed spherically. A calculated model for this difference works well when a concentration of Dark Matter is introduced. There is a hypothesis that galaxies will attract greater amounts of Dark Matter surrounding them than would be found in intergalactic space.
In June, 2003 another report about the action of Dark Matter gave a strong indication of just how much mass is involved. Below is a Chandra view of the galaxy cluster Abell 2029, located about 1 billion light years from Earth. This X-ray image shows a central radiating mass (an elliptical supergalaxy that resulted from merger of multiple galaxies) and a huge cloud of glowing hot gas that is interpreted as under direct control by this Dark Matter, which is estimated to be equivalent to a hundred trillion times the mass of the Sun. In July of 2003 another image was released which may actually show the Dark Matter as a faint glow (arbitrarily rendered by a blue tint) pervading a cluster of galaxies: To obtain this image, the HST was trained for a total of 120 hour of light-collection time on the cluster CL0024 which presently is some 4.5 billion light years away. Spread through the galactic group is the uniform glow which in itself has not been identified as to nature. But its distribution is much as expected for Dark Matter based on theory. If this glow indeed is really a property of Dark Matter, then it produces some luminosity, i.e., emits EM radiation that is normally so weak as to be undetected in shorter exposures of visible wavelength observations from both space and Earth telescopes. Another similar image of two galaxy clusters in HH47 (in the Vega constellation) was released in December 2005 by a Johns Hopkins group. These astronomers used an inventory of stars that bend light to determine that there must be a surplus of Dark Matter (shown in purple) that is needed to allow and maintain the clustering involved. Their interpretion of this matter is that it in the "strange" state wherein individual particles do not collide as they surround the galaxies. The implication is that Dark Matter itself has an uneven distribution in the Universe, tending to be more dense around galaxies and galaxy groups. Here is a defining image published in their report: Another line of evidence for the presence and role of Dark Matter is associated with NGC1404, the Formax galaxy cluster, shown below. The Chandra X-ray image shows galactic gases in blue, heated to as high as 10 million degrees Celsius. The gas clouds are moving at high speeds toward an (invisible) center. The presumption of a large, unseen mass of Dark Matter around the cluster gives the best (theoretically) explanation of the behavior of what has been detected. This cluster may lie at the intersection of two filaments of stretched out Dark Matter; that speculation is in line with the ideas of a network of filaments in the early Universe described on page 20-2. Recently, studies of Dark Matter in the Ultraviolet suggest that one of its constituents appears to be ionized Hydrogen which does not produce a detectable signal from the myriads of Hydrogen clouds now known to populate galactic haloes and intergalactic space. But, chemical processes in these clouds produce ionized Oxygen, uncombined with the invisible ionized Hydrogen, which can be detected. This form of Oxygen is widespread in much of space beyond the galaxies and, together, with the ionized Hydrogen may account for a significant fraction of the daark matter. Another potential approach to studying Dark Matter, including an attempt to prove its existence as commonplace within the Universe (rather than just a fleeting existence during collider experiments on Earth), is now underway with the installation of a 2.8 meter telescope, called the South Pole Telescope, located close to that point in the Southern Hemisphere. It will be capable of measuring small changes in conditions (primarily temperatures) around galaxy clusters; these changes would verify expected variations caused by Dark Matter/Energy as predicted by models now being developed. From the above discussion, one might ask "Where is most of the Dark Matter?". Since it has yet to be found directly, the answer may lie in these possibilities: 1) in Black Holes; 2) in non-luminous galaxies (evidence for a "Dark Galaxy" has recently been reported); 3) present but "invisible" within galaxies; 4) in roughly spherical "halos" around each galaxy; 5) dispersed throughout intergalactic space. An interesting alternative to Dark Matter as the stabilizing force is that of a concept called MOND, for Modified Newtonian Dynamics. This is reviewed by its originator, Dr. Mordecai Milgrom of the Weizmann Institute in Israel, in his article "Does Dark Matter Really Exist?" in the August 2002 issue of Scientific American or the October 2003 issue of Discover Magazine. Check this to be familiarized with its essentials. His ideas are derived from observations that such spacecraft as Pioneer 10, now 9 billion miles from Earth, are slowing down (the expectation would be for increasing velocities as the Sun's gravity weakens with distance). This would seem to imply that solar gravity is actually increasing as the distance lengthens.
In a nutshell, Milgrom postulates a constant of acceleration, called a0, that determines the gravitational behavior of matter. Acceleration values larger than a0 are consistent with the Newtonian Second Law in which F (force) = m (mass) times a (acceleration such as we observe experimentally for gravitational processes or for imposed accelerations [e.g., a rocket launch]). (Recall in the Preface that Newton's Second Law works well on Earth and in the Solar System but is not accurate when galactic scales are involved.) But in his proposal values smaller than a0 modify the behavior of galaxies, including the rates at which they rotate, in a way that obviates the need for Dark Matter's contribution to galactic gravity. Using this non-Newtonian approach, Milgrom's mathematical analysis of galaxy dynamics based on values of a's that are less than a0 reproduces most of the observed effects in the orbital patterns and rates of motion of stars within galaxies. He has tentatively determined that a0 decreases the Newtonian proportionality by one 10-billionth of a meter per second per second. This, rather than Dark Matter, causes stars in a galaxy to move faster than expected. Milgrom's model, initially disregarded by most cosmologists, is now attracting serious attention. An excellent, clearly written article by Martin Rees and Priyamvada Nataranjan, entitled A Field Guide to the Invisible Universe appears in the December, 2003 issue of Discover Magazine As this page has been intermittently added to with new information, we must close our discussion of Dark Matter with two more ideas. One simply contends that "some" of the Dark Matter is Ordinary Matter lying beyond the limits of the observed Universe. This matter then has its own gravitational influence on that Universe as though it were actually within the observed part. Interesting but not readily testable. The second new idea relates to the concepts of Higgs fields and particles (Higgs Bosons) mentioned mainly in footnote 4 on page 20-1. Drawing upon interrelations between particles as treated by the SuperSymmetry model and Higgs fields, theory states that there may exist something called the LSP (for lightest superpartner). The LSP is the decay end product of a series of superpartners (those that can be postulated as complementary to ordinary Standard Model particles) created in the early stages of the Universe. The LSP contains Higgs-induced mass. If real, LSPs can account for much of the Dark Matter. In August of 2006 a claim was made that direct evidence for action by Dark Matter had been found. Astronomers from the University of Arizona and elsewhere, examining the Bullet galaxy cluster using Chandra and other telescopes, were able to determine the mass within the cluster. They observed two kinds of intergalactic material of gaseous/particulate nature that had separated within the cluster. Thus: Their interpretation assumed that within the cluster a smaller galaxy had passed through a larger galaxy (the stars are normally so far apart that few collisions occurred). The larger galaxy should have stripped off matter from the smaller, leading to some segregation. Most of that matter ought to reside in the interstellar gas that provides the bulk of the gravitational forces within the cluster. But they argue that this degree of gravity would be insufficiently strong to keep the galaxies intact during the process. They hypothesized that Dark Matter was needed to preserve the separated gases. If indeed Dark Matter was present in the amount they calculated, then it would bend starlight to a specific extent in the manner which allowed Einstein to prove Relativity. This was observed in about that level. The argument then concluded that Dark Matter rather than the gas was the factor that led to this set of observations. While the proposal is tantallizing, as usual other astronomers have come up with objections and alternate explanations. One such alternative considers gravity to vary in strength over cosmic distances. An even better example of direct imaging of dark matter is this view of two colliding galaxies (official identity: MAGSJ0025). The blue denotes dark matter, as imaged by HST; the red is a Chandra X-ray image of gases: The importance of the Dark Matter concept is that it appears to provide just enough total matter to provide the gravity that holds the Universe together. Those who favor the "Goldilocks Hypothesis" for the Universe's formation - not too hot, not too cold, just right" - argue that too much matter (and/or too little velocity of expansion) would have led to gravitational pull strong enough to counteract the expansion of the Universe, causing it to collapse on itself; too little matter (too much velocity) would have prevented matter from organizing into stars and galaxies. Such results would have been a Universe that did exist but never attained the right conditions for the appearance of biological beings and ultimately humans (and conceivably intelligence elsewhere; next page). Dark Matter seems essential to the formation of stars and galaxies as well. There is insufficient Ordinary Matter to organize and maintain galaxies. Pockets of Dark Matter - whose distribution appears to be related to the ripples or inhomogeneities found by COBE and WMAP - were needed to assist in bringing clots of matter together to start galaxies. Today's galaxies seem held together by higher densities of Dark Matter that comprises the halo around both spiral and elliptical types; this matter also influences the rotational velocities within a spiral galaxy, such that its outer parts move at about the same rates as the inner parts. A painstaking study by an international group of astronomers (NASA, ESA, CalTech) has produced the first 3-D depiction of Dark Matter in a selected region of the Universe. Using Hubble Space Telescope data, they detected this matter indirectly, through its effect on passing light. This yields information on concentrations of Dark Matter at various distances from Earth, using the standard candle approach to determining just how far away is each clump of Dark Matter. In this way they could arrive at how the matter was distributed at different times of Universe history. These two diagrams show aspects of their study: Now, on to Dark Energy per se, which comprises the bulk of the physical entities that make up the Universe. *The steeper sloped H case represents a Universe that is more rapidly expanding, has covered less distance, and is younger (10 billion years); the slope for H = 50 has expanded more slowly over a longer time (20 billion years) but has covered a greater distance (bigger Universe).
The "Missing" Mass in the Universe
Primary Author: Nicholas M. Short, Sr.