## Evidence for the Big Bang:

### The Redshift; Stellar/Galactic Distances; Age of the Universe; Cosmic Background Radiation; Expansion Models; Dark Matter/Energy

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 have already been described: 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; review 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.

Redshift and the Hubble Law

The first derives from relative velocities as divulged by the measured redshift of radiation wavelengths (see below for details). This 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.)

Some of Hubble's observed redshifts led to estimates of galaxy velocities of 100 million kph, about 0.1 the speed of light. Here is a plot of his original data, from which he deduced the expansion concept that later led to the Big Bang model

Hubble noted that, as recessional velocities Vr were measured for stellar sources over a wide range of astronomical distances D, 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. Here is one of his published plots of velocity versus distance.

From Astronomica.org

The resulting straight line plot is easily described mathematically, in the basic equation:

Vr (velocity of recession) = H (the constant determining slope) x D (distance [from observer])

The constant has been designated by the letter H, and is called the Hubble Constant. It is normally given the units of Km/sec/Megaparsec (an alternate form is km/sec/million light years). 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).

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):

From Astronomica.org

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 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. Until recently, one model of expansion is 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.

Let us now look into the details of the concept of "redshift". 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. The pitch of the sound varies systematically, rising on approach (higher frequencies) and then falling as the train 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 analogous to the above Doppler effect. 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).

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 propoortion of older stars) at the time its light left the source 10 b.y. ago . But another considers this 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 their spectral states. 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. The spectra are 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.

This next illustration shows telescope images and spectra from five galaxies at increasing distances from Earth.

From J. Silk, The Big Bang, 2nd Ed.

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; they are white instead of black because the photographic plate is printed as a negative) obtained by spectroscopic analysis of a sample on Earth. 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 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 second spectral image, the horizontal arrow leads to the position of the line pair 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 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.

Source: M. Corbin

The displacement of a spectral line owing to redshift can be used to calculate the 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 formula:

z = (λobs/λrest) - 1

Using the z value, the velocity v of receding motion of the source is given by:

v = cz (1 + 0.5z)/(1 + z)

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. This range of possibilities is pertinent to the accelerating Universe model discussed on the next page.

A variant of this is shown in this figure:

The ordinate denotes relative age: At this time, that can be given by "1", with those nearby galaxies that appear most fully evolved (to 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.

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. 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:

Stellar and Galactic Distances (from Earth)

To apply the redshift to estimate R (Scale Factor), and to determine the Hubble contant H, the distances to the shifting bodies must be specified. 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. 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.

Redshift measurements for more distant starlike bodies are actually made on galaxies (their individual stars may not be resolvable) whose luminosities are the average of all component stars. Approximate distances to much 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 characterist 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 group 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 of the type Cepheids (δ-Cephei).

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:

m - M = 5(log d/10)

In the 1920s, Edwin Hubble more 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 (they have varying degrees of accuracy. Use of multiple methods applicable at different distances is called the Cosmic Distance Ladder. To sum up: Among these methods are (in order of usefulness at increasing distances: 1) Parallax; 2) Moving Cluster; 3) Color-Magnitude; 4) Period-Luminosity (Cepheids); 5) Supernovae. This diagram shows several of these and some other methods; the abscissa in the chart is in units of Megaparsecs. A good, in-depth review of the principal methods used in distance determination is found at Ned Wrights Cosmology site.

From Astronomica.org

The Cosmological Redshift z is given as: z = (rec - em)/ em = Vr/c, where em is the wavelength 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, and c is the speed of light. (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

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:

From Astronomica.com

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:

Dnow/Dthen = Rnow/Rthen = z + 1 = λrec/λem,

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.

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, the present-day value of H (i.e., H0) had fallen to 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 H - 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).

Cosmic Ages

The general relation for the Universe's age (since the Big Bang) is given by the expression: t0 = 1/H0. In the actual calculations, when H units (in the Mpc mode) are adjusted to give an answer in billions of years, the formula becomes: Age = 977.8/H0. For an H0 of 65 km/sec/Mpc, the formula gives an age of 15.04 billion years (estimated uncertainty is +/- 2 billion years). Currently,

13.5 billion years (H0 = 72.5 km/sec/Mpc) is the most widely accepted value (ages between 14 and 15 billion years are also quoted in papers published in the last few years). The lower the value of H, the larger is t0 and thus the Universe becomes older.

The formula t0 = 1/H0 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 = 70 km/s/Mpc (s = sec; Mpc must be converted into mega-light years):

t (109 years) = 1/70 km/s/Mpc x 3.26 Mly/Mpc X 106 ly/Mly X 9.46 x 1012 km/ly X 1/3.15 x 107 s/year = 14.02 billion years

(Note: / denotes values to its right are in the denominator of that term; X is the multiplier sign between terms.)

However, the Hubble Age also depends 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. 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.

Over the past 5 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 H range they arrived at, an age of 12 to 13.5 billion years would result. 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 the most 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.

Most astronomers disputed the above age conclusion based on the galaxy distance model, citing older ages according to their calculations and their interpretation of H values using different inputs. In the last few years most cosmologists (e.g., Alan Sandage and associates) are advocating a value of H that yields an age closer to 14 Ga; this recent age is now the preferred "best estimate". 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 H 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 known lie well within the limits of the knowable Cosmos. Said another way: there may be considerably more space beyond our present observable Universe, that 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.

The first reported (before 1995) HST-derived ages fell between 8-12 Ga, anomalously low compared with pre-Hubble reported ranges of 12 - 18 Ga. This was especially confusing in that separate evidence and theoretical calculations indicate some distant galaxies might well be 13 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 billion l.y., and possibly a few yet to be detected that are even farther away (older) (page 20-8), must lie near the observable edge of the Universe.

Thus, 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 *.

The critical 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 (i.e., 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).

As implied above, the farthest galactic-sized objects found to date are about 13 billion l.y. from Earth . These most distant sources yet detected have a redshift z verging on 5.8 (reaching to about 90% of the speed of light) and represent galaxies that formed in the first billion years or so after the Big Bang. 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).

The time at which such large sources of detectable luminosity is sometimes cited as the Friedmann time, taken as the narrow time span when stars first formed and collected in significant groupings. These often contain quasars that presumably grew from young (protogalactic) gas clouds which at the time were emitting photons at an observed temperature of ~3,000° K (referenced to an idealized blackbody - one which completely absorbs incident radiation of all wavelengths and acts as a perfect emitter; at that temperature, the wavelength signature peaks at ~1 µm, however, at higher z values the actual blackbody temperatures can be much higher, causing a peak in the ultraviolet).

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 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 decrease in redshift accompanies the expansion of the Universe. The process of enlarging space leads to a lengthening of the wavelength of light - hence the progressive drop in the redshift value of z. Since redshift also 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.

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. 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 (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 now that an upper limit of 14 billion years will stand as the actual age of our Universe.

Cosmic Background Radiation

Another solid proof for the Big Bang was the discovery that Cosmic Background Radiation (CBR) 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 wavelength expected from a radiant blackbody source whose temperature is now 2.72° K. George Gamow and his colleagues had first predicted such radiation (their estimate of its peak was at 5° K) in 1948. The CBR now evident as pervasive throughout space 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 at approximately 6 months after the Big Bang. Evidence of what it was doing during the Radiation Era, up to Decoupling, is 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 300,000 years. At that time, as the temperature dropped to about 4000 °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 B.B. With the resultant transparent Universe, CBR first became detectable, displaying the higher temperatures it then possessed in the still early Universe. From Decoupling to the present time, the CBR has experienced a redshift of ~1200.

The photon radiation 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 B.B. 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 short 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; 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 then confirmed by R. Dicke and his group at Princeton. This test, 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 critical foundation concepts that support and explain the Big Bang in its present form. Further discoveries will likely lead to refinements but the fundamental concept and the proper numbers predicted from the general model now seem to be solidly substantiated.

The value of satellites in this refinement process is well illustrated by COBE (Cosmic Background Explorer), launched in 1987 (check out its current Internet site). 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 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. And, COBE took extremely accurate readings over much of the wavelengths involved in the blackbody curve determined experimentally for a 2.726° K body, demonstrating that the background radiation fits that curve at better than 99% accuracy (an astounding achievement seldom attained in most scientific measurements). 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) 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).

A variant of this includes measurements made by other CMR measuring experiments (different systems).

COBE also 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 100000 during the first billion years after time zero. The maps below show the broad distribution of minute temperature differences 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.

These results are confirmed, with more detail, by the CBI (Cosmic Background Interferometry) experiment run jointly by CalTech and the NSF. Thirteen 1 meter diameter dish antennae are synchronized in an array with a broad baseline. This next figure is a map of the background radiation over an area equivalent to about 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 when the CBR was around 6000° K. Associated with these differences are variations in material density. This observation supports the idea that matter in the Universe at this early time was unevenly distributed, thus allowing the first stages of density/gravity variations required to initiate the galaxy formation process. The data displayed in these 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.

The results from COBE proved of such import to understanding the early Universe, especially the small but critical fluctuations it detected, that a more sophisticated satellite, MAP (Microwave Anisotropy Probe), was launched in July of 2001. Background information on this important new astronomical observatory can be found at NASA Goddard's MAP site. (Another CBR satellite, the Planck Surveyor, is planned for launch no earlier than 2005.)

The long-awaited preliminary results from MAP were announced at a press conference on February 11, 2003. Prior to that MAP was renamed WMAP, honoring the late David Wilkenson, a leader in the field.

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. 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 +/- 1% is claimed) age for the Universe of 13.7 billion years. Another is strong confirmation of the reality of Inflation during the first fraction of a second after the Big Bang. The amount of detectable ordinary matter in the Universe has been reset at 4% whereas dark matter is 23% and dark energy 73% (but the results offer no clear indication of the nature of these dark states). The time when the Universe first became transparent is now given as 380000 years after the B.B. Further evidence for accelerating expansion is derivable from the data, leading to a firm conclusion that the Universe should expand forever. Finally, many of the fundamental physics and cosmological parameters have been refined, as shown in this table (without any attempt by the writer to identify each).

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 ago. The first galaxies began to organize some three hundred million (300,000,000) years later. This diagram depicts these stages (from top): 1) initial stages of CBR variations; 2) clots of dark 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.

Some cosmologists attending the press conference went on record as believing the WMAP results will prove to be the most important new data sets obtained from observations over the last decade.

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 will seek 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.

### Models for the Expanding Universe

Models of the Universe can be classified in several ways: 1) Newtonian vs Relativistic; 2) with or without a Big Bang, i.e, expanding vs steady state; and 3) for the Big Bang models, these are either Standard or with a Cosmological Constant.

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 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 influenced 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 - 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 based on the idea underlying the Hubble Length, which is just the distance outward from Earth, as an arbitrary center (remember, the Universe actually has no meaningful center), that has traveled in 1 Hubble time (tH = 1/H). In this framework, that distance is represented as the farthest out we can look from Earth with our best telescopes to see the first evidence of the Big Bang (which is not really possible owing to the opacity soon after the B.B.); it is closely related to lookback time, defined above. Consider the Hubble distance to be the radius r for a sphere that encloses all of the Universe that we can presently see (this seems legitimate in that currently the farthest galaxies [only a few found so far] all seem to be about the same distance in light years from our observation point; these distances are somewhat less that the outer limit that is defined by the current value of H0). A simple way to visualize this sphere with its contents is to imagine the points within (galaxies) such that the farthest away (representing star systems in their earliest years are colored blue, intermediate green, and closest (more advanced in development [but not necessarily any older or younger than the blue group]) as red. The occupants of the Hubble Sphere would thus show concentric color bands with blue closest to the sphere boundary and red closest to the center. That 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".

Using this simplified, rather easily visualized model, let us take a moment to 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 no 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 point 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 so much in 14 billion years. Euclidian size is not a valid way to look at the Universe, whatever "shape" it may have, as implied from the paragraphs further 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.

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 - 13+ 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 (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.

Now, to survey the major models for the spacetime Universe:

Relativity has played a vital part in the models of the Universe that remain the most plausible. The expansion of the Universe from a relativistic framework can be summarized as the Friedmann equation. We give it here in two forms, the first as a differential equation:
dR/dt = (8 Π G)/3 ρ R2 - kc2

And the second:

H2 - (8 Π)/3 G ρ= - kR2

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, 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 and isotropic (essentially the same average distribution of matter/energy in all directions) on the largest scales (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 (B.B.) 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.

MODEL | GEOMETRY (k) | L | q | FATE
de Sitter | Flat (0) | >0 | -1 | No B.B.; exponential expansion; empty
Steady State | Flat (0) | >0 | -1 | No B.B.; 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 augments gravity. Lc is one particular number known as the critical value. 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 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 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

This next plot is a recent display of the curves for various models in which the ordinate is the relative brightness (luminosity) of galaxies used as data points. (The dark energy case is discussed on the next page).

The nature and shape of the Universe depends on its mass density (including energy forms that have mass). The key parameter is the Critical Density, symbolized as ρc (ρc = 3H3/πG). This is defined as just that total mass 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. (As a practical measure it is estimated that, if all atomic matter - both galactic and intergalactic - is redistributed to spread uniformly through space, its density will average 10 atoms per cubic meter.)

There are three general 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?

#### This figure was copied from Nick Strobel's Astronomy Notes. Go to his site at www.astronomynotes.com for any updated versions.

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. 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 space-time cone figures, such as this one, showing from left to right the steady, decelerating, and accelerating expansion models:

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.

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 >, =, and < 1 respectively.

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.

The first five models are all non-standard and were devised when Einstein's Cosmological Constant seemed to have some essential validity (abandoned,by Einstein and the cosmological community in the 1930s but now reinstated; a good review of the present status of the Constant is found at this University of Chicago site). Each of these models fits at least some of the general observations of the Universe but failed on other accounts. Einstein himself spent many years in calculating properties of such Universes but eventually abandoned the concept of a counter-gravity force, admitting it was his "biggest mistake" in his scientific reasoning. Evidence for this Constant is still lacking but in recent years variations of it 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 vacuum energy density may 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.

The Einstein Universe is a static one, with spherical geometry, developed 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. 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, Steady State 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"; 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 (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 (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) with decreasing rates of augmentation thereafter. 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.

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 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. Results from COBE and WMAP seem to offer solid support for this view. 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.

### The "Missing" Mass in the 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 critical 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. 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 count quantitatively. Dark energy, a closely related topic, is mentioned briefly in this subsection but will be examined in some detail on the next page.

As will be discussed below, some of the dark matter seems to associate with the galaxies. But a computer simulation reported in late 2003 indicates the bulk of dark matter occurs in large "clumps" distributed throughout intergalactic space. Black holes may serve as collectors of this dark matter.

A recent estimate states outright that the several kinds of dark matter, and dark energy, together comprise ~95% of the Universe's mass, with varieties of normal matter accounting for the remaining less than 5%. This means that most of the matter in the Universe presently is invisible to detection so far on 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 starts in a gravitational bind.

Another line of evidence comes from the gravitational lens effect - 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 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 and a size estimated to be more than 2.5 million Sun diameters 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 provide 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 white 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 helum 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) 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 is 100,000,000 to 1. Despite miniscule mass, the total from so many neutrino particles would make a sizeable contribution to the total (still unaccounted for as specific components) mass of the Universe.

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 SuperSymmetry theory.

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 matter and energy (which can be expressed as matter using the E = mc2 conversion) 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:

A similar diagram, made a few years later, shows a slightly different composition, owing in part to selection of different categories of the physical components of the Universe:

In this diagram, Ordinary visible "matter", mainly in the galaxies, amounts to only 0.5%. Photon radiation moving about the Universe contributes just 0.005%. The MACHOS make up the Ordinary nonluminous matter (3.5%) and WIMPS comprise the Exotic dark matter(26%). The bulk of the ingredients in the Universe is what is known as "Dark Energy", and accounts for ~65% 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 corresponding 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.

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 around the Sun have been proposed.

One test for the existence of Dark Matter (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 up to about 5 times the radius of each galaxy examined so far.

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 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 further generalization: Dark matter surrounds all galaxies and serves to keep them intact. In effect, it provides the added gravitational influence that maintains galactic coherence (the stars, dust, and gases alone would be insufficient to prevent the galaxies from flying apart).

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 of on 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 many galaxies) and a huge cloud of glowing hot gas that is interpreted as under direct control of this dark matter, which is estimated to be equivalent to a hundred trillion times the mass of the Sun.

A few of the galaxies within Abell 2029 are depicted in this visible light image made by the Palomar 48-inch Schmidt telescope.

In July of 2003 another image was released which may actually show the dark matter as a faint glow (blue) 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 (map) is much as expected for dark matter based on theory. If this glow indeed is really 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.

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, is now underway is 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.

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 8 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, he 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) time 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 gravity. Using his non-Newtonian approach, his 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. His model, initially disregarded by most cosmologists, is now attracting serious attention.

Some of the ideas introduced on this and the preceding page are examined in a different manner, based partly on the information provided by the Cosmic Microwave Background Radiation, on this Internet page prepared by astronomers at the University of California, Santa Barbara. (It is rather technical.) Two other reviews on cosmic expansion and Einstein's Cosmological Constant, prepared by Sten Odenwald for the Raytheon Corp., are found at (1) and (2). A good review of Dark Matter and Dark Energy appears in a Science News Web article.

An excellent, clearly written article by Martin Rees and Priyamvada Nataranjan, entitled A Field Guode to the Invisible Universe appears in the December, 2003 issue of Discover Magazine

Now on to Dark Energy per se, which comprises the bulk of the 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).

Primary Author: Nicholas M. Short, Sr. email: nmshort@ptd.net