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 = (λ_obs/λ_rest) - 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 = V_r/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), V_r 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(t_em) - 1 describes the redshift in terms of the Scale Factor R pertinent to t_em which refers to the particular time when the light was emitted . This relationship can also be cast in the following way:

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 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:

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 300,000,000 million 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) are shown in this diagram

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 were first 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 of 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 (t_H = 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 r_H. 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 (D_H), 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 D_H, 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 D_H, 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 D_H 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:

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).