Evidence for the Big Bang and the Expansion of the Universe Part-6 - Completely Remote Sensing, GPS, and GPS Tutorial
Evidence for the Big Bang and the Expansion of the Universe Part-6

In July of 2010, the Planck team released the first full sky map made by the Planck telescope. Most of the blue in this map is associated with the Milky Way galaxy. Much of the CBR is rendered in red. A few anomalies are evident but it will take up to 2 years for the team to produce details of variations within the radiation.

The first full sky CBR map made by the Planck Observatory.

This is a low resolution map. Planck can produce false color composites of selected regions using any 3 of the 9 bands in its sensor. These show much detail. Two examples are the Orion Nebula and star formation in the Perseus cluster. Their locations are indicated in the circular map shown first:

Location of Orion (left square) and Perseus (right rectangle) images, seen beneath.
Orion Nebula.
Perseus cluster.

Planck will produce a series of image strips covering the entire sky that will become available in (or soon after) 2010. The resolution will be superior to that of WMAP. This should aid in improving our understanding of the state of the early Universe.

Evidence for the Expanding Universe

The modes of behavior of the Universe over time can be classified in several ways: 1) it follows either Newtonian or Relativistic physics; 2) it commenced with or without a Big Bang (i.e, expanding vs steady state); and 3) for the Big Bang case, the growth has been controlled either by Standard Model physics or has been influenced by the Cosmological Constant (or both?).

As a fundamental conclusion drawn from the general acceptance of the Big Bang model for the Universe's origin and development, the initial small space that developed in the first minute has been continuously enlarging - a process analogous to expanding in the manner described on the previous page. However, the precise nature of this expansion, still not fully known, depends on the specific expansion model, as we shall see below. This is related to the amount of mass/energy available to control or influence the expansion. As we will see in the following paragraphs, proposed geometries of the expanding Universe range from spherical to hyperbolic to flat. The duration of expansion ranges from finite to infinite. The terms "open, closed, flat" refer to certain constraints on the curvature of space and on its expansion history.

The type of Universe "shape" model - open, closed, flat, spherical - is a factor in the change in the Hubble constant (and the corresponding redshift) with time. A generalized relationship depending on expansion models is shown in this next plot:

Velocity plotted against distance to give a straight line plot of the Hubble curve for parts of the Universe closer to Earth; departures from linearity are depicted on the right as generalized for the space expansion models that depend on the amount of matter in the Universe.

Before reviewing the various models that were proposed in the 20th Century, we pause to briefly describe a useful and (deceptively) simple view of the Universe embodied in the term Hubble Sphere. This is almost a synonym for "observable Universe" but with one unique property. The sphere moves - it is just that which can be observed at any arbitrary point in the Universe. Earth has its own Hubble Sphere. But a planet in a galaxy 5 billion light years is another arbitrary point and has its own Hubble Sphere. The sphere at each such point has its Hubble Length, which is just the distance outward from the observing point, as an arbitrary center (remember, the Universe actually has no meaningful center), that light has traveled in 1 Hubble time (tH = 1/H). In this framework, that distance is represented as the farthest out that a particular observer at a point can look with the best telescopes to see the first evidence of the Big Bang (which is not really possible owing to the opacity soon after the BB); it is closely related to Lookback time (time for light from an emitter to reach Earth or any other point of reference). Consider the Hubble distance to be the radius r for a sphere that encloses all of the Universe that can presently be seen. That outer limit boundary is, of course, a time horizon and not an actual physical surface encompassing the sphere. As we progress into the future and our instruments "see" still farther, the apparent surface of the sphere moves outward with the increase in rH. There are galaxies beyond the Hubble Sphere; they just haven't been seen yet but will come into view later. Beyond the outermost galaxies, assuming they occur at light year distances equivalent to that of a precisely known Hubble Age, we cannot as of now specify "What's there".

Let us now say a few things about the size of the known Universe. It would seem to be determined by the Hubble Distance (DH), which relates to the Hubble Age, around 14 billion years. This is the distance out to the event horizon, the farthest out in spacetime that we can see discrete particles or objects in the Universe. To quantify the distance in Earth kilometers [or miles], just multiply the distance that light travels in 14 billion years by the speed of light. Thus: 14,000,000,000 b.y. x 300 x 104 km/sec x 3600 sec/hour x 24/hrs/day x 365.4 days/year. For this case, the result, which I will call DH, is 1.3245 x 1024 km, or about 1.3245 septillion kilometers.) From the Hubble Sphere model, one might assume that the sphere has a diameter of 2 x DH, particularly when one is aware that the event horizon is essentially the same looking outward, say from the North Pole at the northern celestial sphere and from the South Pole at the southern celestial sphere.

But, this is not so. In relativistic space expansion, the distances outward in opposite directions from the Earth framework are not additive. This is due to the fact that all points in the singularity that are now galaxies were next to each other at the beginning and have simply drawn apart with the expansion of space. With no meaningful center, we can only state for now that space has expanded some finite amount in 13.7 billion years. Euclidian size is not a valid way to look at the Universe, whatever "shape" it may have, as implied from the paragraphs later on this page. In trying to think about "size" there is a further complication. The expansion during the Inflation period (see page 20-1) may have proceeded at rates faster than the speed of light. If so, the Universe may really be much bigger than what we deduce from event horizon distances. We get our idea of distances only from measurements of z and H as determined from we see now in the Universe after the galaxies formed. Prior to those times, inflation expansion, yielding much greater z and H values, could have pushed the outer edge of the Universe to distances well beyond what can be detected as apparent event horizons.

One interesting corollary to this reasoning is that in principle cosmologists can detect galaxies that appear to be receding as speeds that when calculated seem to be exceeding the speed of light. This is because the Hubble constant isn't constant, it is increasing. This apparent contradiction to Einstein's relativity demand that light has one fixed finite value is explained on pages 40 and 42 of the previously cited Misconceptions about the Big Bang, by C.H. Lineweaver and T.M. Davis, Scientific American, March 2005.

So, what can we say about our understanding of the size of the (our) Universe. Its minimum size must be at least as far out in spacetime as we can see galaxies, quasars, and supernovae - 14+ billion light years to the currently known event horizon. We cannot [yet] see timewise to anything before the Radiation Era; Cosmic Background Radiation, which traces to about 300,000 years, is pervasive and thus not location-specific. The maximum conceivable size is infinity, with "outer limits" reachable only in infinite time. If the Universe is indeed infinite, its present outer limits are not fixed in any way, as they will enlarge forever in their expansion towards infinity. If the Universe is proved to be finite (possibly contrary to the most likely scenario - see below), then its boundary is almost certainly beyond the event horizon we now see - there are more galaxies farther away which will become visible as time progresses and DH lengthens. The safest conclusion now reached under currently postulated scenarios is just that the Universe must be larger than the presently determined horizon distance.

But thoughts on size are changing. We can set a lower limit of the observable Universe at the currently most favored age of 13.7 billion years, that is, we can now see out to that part of the outer Universe that contains all the stars within a "sphere" in which light has traveled no longer than 13.7 billion years at its present speed. And we see that value in any direction we look. Perhaps this means that we are near the center of a finite Universe. If so, its diameter would about 29.4 billion years. But when the fact that the Universe is now accelerating (as discussed on the next two pages), this must be taken into account.

Dr. Neil Comish and colleagues at Montana State University have done a preliminary calculation on how much the Universe has expanded since the first radiation around 13+ billion years was released and is now just being received on Earth. But because the Universe has expanded tremendously since the Big Bang, the distance that light has been traveling continues to increase during the 13+ billion year timeframe. The source of the primordial light leaving the very early Universe from any point (say, the first star), has thus itself moved much farther than the time-travel distance. Their model leads to an astounding number - 78 billion light years to the edge of today's Universe and a possible diameter of a spherical Universe of 156 billion l.y. (so large both because of the effects of spatial expansion and acceleration rates since about 6 billion years ago. One might conclude that this requires different values for the speed of light in the past, which might seem to violate the General and Special Laws of Relativity, but the astronomers point out that this speed remains constant while the distance a photon released at the beginning of the Universe must travel is what is increasing. This estimated diameter and other figures for size are obviously still controversial but the "true" size should be increasingly refined in coming years.

A summation: Lets say that we detect a galaxy that is 13.5 billion light years away. It has taken that long for light near the dawn of cosmic time to reach Earth. Is that the size of the Universe? An emphatic NO! It must be larger. At the time of light departure, the actual Universe THEN was much smaller - about a 1000 times less than at present. Over the 13.5 b.y. travel time, the Universe has expanded (not at a uniform rate but with the decreasing acceleration in its first half of existence and now replaced by an increasing acceleration, as described on the next page). The important point is that growth of the Universe during the 13.5 b.y. time of travel has stretched out the actual size even as the light had to continue to make its way to Earth observers. The fact that this burst of light 13.5 b.y. ago ultimately reaches us happens because the total growth rate is notably less than the speed of light. Relativity is built into this description (consider the analogy of one walking from one end of a train to the other even as the train moves along track; the total distance traveled is some combination of person walk plus train progress). Hopefully, this paragraph may clear up any uncertainties you retain after working through other relevant parts of this Section. But, if you would like more information on the size and shape of the Universe, consult this Wikipedia website that discusses the Observable Universe.

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 (in terms of rate of change of the Scale Factor R = r/r0) from a relativistic framework can be summarized as the Friedmann equation. For the distribution of matter in the Hubble sphere, the equation considers the contributions of both the gravitational potential energy and the kinetic energy of expansion. We give it here in two forms, the first as a differential equation:

(dR/dt)2 = (8 Π G)/3 ρ R2 - kc2

And the second (introducing H):

H2 - (8 Π)/3 G ρ = - kc2/R2

In these equations, Π (pi) is the familiar constant (ratio of a circle's circumference to its diameter = 3.14159...), G is the Universal Gravitational constant (6.6726 x 10-11 m3/kg/sec2), ρ is a Greek letter denoting the average density of the Universe, k is a curvature constant in which values of 0, +1, -1 represent flat, spherical, and hyperbolic geometries respectively, R is the Scale Factor for the observable Universe, H is the Hubble Constant, c is the speed of light, and t is time. A solution to the Friedmann equation depends on which Universe model is being tested, as the group described next has different values for key parameters.

Several cosmological scenarios, named after the scientist(s) who first proposed each (several scientists came up with more than one model), for various modes of expansion lead to different end results (shown graphically below for four general models).

Four general models for different expansion histories of a Universe driven by the Big Bang.

In common, they all obey the Cosmological Principle, which states that the Universe is both homogeneous(defined as being the same at any point within space) and isotropic (as one looks out, appearing the same in any direction. This boils down to having essentially the same average distribution of matter/energy in all directions) on the largest scales (500,000 light years and larger. This is not violated at the scale of galaxy clustering since at the universal scale these tend to be "smoothed out" by having much the same patterns anywhere one looks. Open models also must be consistent with the restriction placed by the Second Law of Thermodynamics which from a cosmological standpoint states that over time the entropy (a measure of disorder of a system) must ultimately increase to (or towards) a maximum (total disorder). Interpreted at a universal scale this would lead to complete dispersal of galaxies and their stars (perhaps rearranged as randomly distributed Black Holes) and blackbody temperatures approaching zero. A corollary holds the initial singularity to have minimum entropy which then rapidly increases during the first moments of the Big Bang.

Note that when the above curves are extrapolated back in time, they strike the horizontal axis at different positions (times). This means that the age of the Universe will vary relative to the particular model being considered. Thus, although the current Hubble time (1/H0), which depends on the accurate determination of the rate of expansion, leads to an age or duration of the Universe, that value can be modified when (and if) a particular expansion model is shown to be the best or valid one.

The following table (modified from Hawley and Holcomb, 1998) summarizes the principal Cosmological Models that have been developed and tested by calculations. They fall into two groups: Non-Big Bang and Big Bang. Another distinction category: Models in which the Cosmological Constant L (see below) is a factor (upper five rows of table) and the Standard Friedmann (or Friedmann-LeMaitre) models in which L is not involved (i.e., is O; bottom three rows); the three standard models also have Deceleration Parameters q (defined below) that include the value 1/2 in some way.

de Sitter Flat (0) >0 -1 No BB; exponential expansion; empty
Steady State Flat (0) >0 -1 No BB; uniform expansion
Einstein Spherical (+1) Lc 0 Static; H = 0; now, gravity balanced by repulsive force; may be unstable
Lemaitre Spherical (+1) >Lc <0 Expand; hover; expand
Negative L Any <0 >0 Big Crunch
Closed Spherical (+1) 0 Big Crunch
Einstein-de Sitter Flat (0) 0 ½ Expands forever; density at critical value
Open Hyperbolic (-1) 0 0 Expands forever

q = The Deceleration Parameter: denotes the rate of change with time of the Hubble Constant and R; a positive value indicates acceleration; negative = deceleration.

L = The Cosmological Constant, introduced by Einstein to his field equations for General Relativity in order to provide some constraint to gravity (a counter-effect) to avoid an inevitable collapse of the Universe; if + (repulsive) L counteracts gravity; if - (attractive) L may be equivalent to the vacuum energy density associated with particles at the quantum level. (L in texts is also given by a capital Greek letter Λ). The current value for energy density within the observable Universe is between 1 and 5 x 10-26 kilograms per cubic meter.

The Steady State, de Sitter, and Einstein Universes, all non-standard, are currently not supported by observational evidence.

The more general diagram above showing four alternative expansion models can now be redisplayed in terms of the names associated with some of the specific models described in the above table:

 Diagram illustrating several of the principal models for expansion of the Universe with time.

From J. Silk, The Big Bang, 2nd Ed., © 1989. Reproduced by permission of W.H. Freeman Co., New York

The nature and shape of the Universe depends on its mass density (including energy forms that relate to mass according to the E = mc2 equivalency). The key parameter is the Critical Density, symbolized as ρcrit, and is calculated as ρcrit = 3H2/8πG. ρcrit is derived from the Friedmann equation; conceptually, it is the amount of matter/energy needed to lead to flat spacetime, in which the Universe is neither open or closed. Using the current value of H as 22 km/sec/Mly, ρcrit is 9.7 x 10-27 kg/m3. Since Hydrogen is by far the most abundant element in the Universe, ρcrit can be presented as an average of 5.8 atoms of H per cubic meter. ρcrit is postulated to be just that total mass/energy that causes the Universe neither to expand forever nor to collapse on itself, i.e., it is flat and will just stop expansion after infinite cosmic time has elapsed. Thus, a flat Universe is one that expands at the "balanced rate" that permits it to just avoid an eventual collapse.

Ω is a fundamental parameter that is the ratio of the actual density to the critical density. In terms of the Friedmann equation, Ω = ρ/ρcrit = 1 + kc2/H2R2; k is a measure of curvature and R is the radius of a Universe considered to be spherical . Ω values have been determined for all the prime constituents of the Universe and have these (approximate values). Ωde (dark energy) = 0. 73; Ωdm (dark matter) = 0.23; Ωat (atomic matter) = 0.044; Ωph (photons) = 5 x 10-5; Ωnu (neutrinos) = 3.4 x 10-5. These will sum to Ωtot (total) = 1. In the more general case, Ω is often expressed as ΩΛ for all Dark Energy and ΩM for all matter, both Dark and Ordinary.

In the more general case, Ω is often expressed as ΩΛ for all Dark Energy and ΩM for all matter, both Dark and Ordinary. The history of ΩΛ and ΩM over cosmic time has been one of progressive increase of the first at the expense of the second. Thus, ΩM was nearly one (1) at the beginning of the Universe and now has diminished to 0.27 (0.23 for Dark Matter and 0.04 for Ordinary Matter) will continue to decrease in the future as ΩΛ increases beyond the present 0.73, causing ever increasing expansion.

As a practical measure it is estimated that, if all atomic matter - both galactic and intergalactic - is redistributed to spread uniformly through space, its mass density will average just under 6 atoms per cubic meter. This is notably lower in the parts of space far from galaxies. This near vacuum space will contain mostly Hydrogen atoms. The least populated parts of intergalactic space are "almost totally empty", not quite a true void having about 1 atom per cubic meter, but consists of Hydrogen atoms, traces of other atomic species, ions, infinitesimal amounts of ice and dust (including possible organics), virtual particles and Dark Matter/Energy - all in very low amounts. The intergalactic density distribution also likely varies, becoming higher as galaxies are approached. Individual stars and nebular clouds are found in parts of intergalactic space as local regions of concentrated matter.

There are three general density-controlled shapes available as options for the configuration and expansion of the Universe. Their geometric characteristics are depicted in this next figure. Note that two properties help to define the nature and behavior of each shape: 1) What happens to so-called parallel lines in traversing the shape, and 2) What is the sum of angles in any triangle drawn on the shape?

Three fundamental shapes that an evolving Universe might adopt.

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. Spherical, flat, and hyperbolic space have this defining property in which the sum of the angles in a triangle are greater than, equal to, or less than 180° respectively. In flat space, parallel lines remain parallel in this geometric sense; this provides a means to test the type of Universe geometry that corresponds to reality. This implies that light beams from a distant source do not converge or diverge. So far, evidence is that lines of radiation travelling in space remain parallel unless disturbed by gravity from massive bodies. Both flat and hyperbolic space can extend indefinitely (to infinity) in contrast to spherical space (but, in principle, if it expands continuously forever that too could lead to a kind of infinity).

These three general types of shape can also be depicted in spacetime cone figures, such as this one, showing from left to right the steady, decelerating, and accelerating expansion models:

Cone diagram (space expansion condensed to two dimensions; time increase shown vertically; Left = Uniform expansion; Center = Decelerating expansion; Right = Accelerating expansion.

From the above, one theoretical way to distinguish which shape best describes that of the Universe: send two light beams oriented parallel to each other but separated by some distance. In the flat Universe, these beams will always remain parallel. In the hyperbolic Universe, the beams diverge; in the spherical Universe they will eventually converge and cross each other. (Theoretically, the test could be compromised by the beam being affected by strong gravitational forces, as has been demonstrated for predictions made by Einstein's General Relativity.)

If the the total density (choosing M as the sum of all matter and all energy; remember that energy can be stated in terms of mass by Einstein's famed equation, restated: m = E/c2) distributed throughout a finite Universe of some size or volume V is less than the Critical Density, space is hyperbolic and open; if greater than critical, spherical and closed; and if equal to critical, space is flat (at least at the scales we observe it). This can also be expressed as the Density Parameter or Ω which is the ratio of the actual densities ρ of matter and energy present in the Universe to ρc, the density that would apply to a Flat Universe expanding to infinity. The Open, Flat, and Closed Universes are associated with Ω > 1, = 1, and < 1 respectively.

Each of those models fits at least some of the general observations of the Universe but has failed on other accounts. Considering all of these models: If the Universe is open or flat, the Universe will expand infinitely but at different rates depending on the parameters associated with each model. The closed and negative L models, in contrast, predict finite expansion followed by eventual contraction and thus at some time the Universe returns to a singularity state. For each of the models, the expansion geometry and the behavior from the onset (the Steady State model has no "beginning") to its eventual fate (Crunch; Expansion) depends ultimately on the matter density that characterizes it.

As stated earlier on this page, the presently favored model for the Universe's geometry is "flat" (although an Ωtot of 1.02 [see table above] suggests it may be slightly open). This seemingly contradicts the notion of expansion of a sphere. But when the size of the sphere is huge (radius estimates vary but can be greater than 42 billion light years), if one is located at any point "on" the sphere, the curvature is so slight that the "surface" appears flat. The relevance of "flat" is that it describes a geometry that is Euclidean.

The first five models are all non-standard and were devised when Einstein's Cosmological Constant seemed to have some essential validity.

This is an appropriate point at which to elucidate this famed Cosmological Constant. Einstein himself spent many years in calculating properties of various Universes. Einstein favored a static Universe (neither expanding nor contracting). But gravity should cause the Universe to eventually collapse. To offset that effect, Einstein postulated a form of vacuum energy density that would be positive in the sense of countering gravity (in a sense, causing offsetting expansion that just balanced to contraction from gravity). This he named the Cosmological Constant. It is usually represented by the Greek letter Λ and is expressed in this equation, in which ρ is the density term, G is the Universal Gravitational Constant, and c is the speed of light:
The Lambda equation

He introduced Λ to his field equation that described the Universe's status in terms of the Friedman model (see above), yielding this equation:

Einstein's modified field equation.

When Hubble and others presented ever more convincing evidence that the Universe was actually expanding, Einstein refuted his Cosmological Constant, calling it the "greatest blunder of my life".

In recent years variations of the Cosmological Constant are again becoming fashionable to explain some of the phenomena essential to a changing Universe, as we shall see on the next page which dwells upon an Accerating Universe. Its possible equivalence to the concept of u>vacuum energy density that may be the nature of Dark Energy (next page) has rehabilitated the idea. It may also have been a key factor in the Inflationary Stage of the early Universe; a rapid increase in L (the Lambda-force) could be the driver behind the tremendous expansion then but that increase had to be short-lived and L must revert towards zero or the Universe would have long since "blown" away.

Values for Λ are hard to come by even in modern textbooks. The current values are associated with vacuum energy density. The ones quoted in the Wikipedia web site on the Constant are "on the order of 10-35 s-2, or 10-47 GeV, or 10-29 g/cm3,[5] or about 10-120 in reduced Planck units."

The Einstein Universe is a static one, with spherical geometry. It was put forth by this great scientist as an attempt to apply General Relativity to Cosmology. The idea of the Big Bang had not yet captured the attention of cosmo-scientists. In order to keep the Universe "going" instead of collapsing under its own gravity, Einstein invented his Cosmological Constant L to balance the attractive forces. While now considered notably incorrect, this type of Steady State model stimulated others to propose variants that incorporate expansion. The de Sitter Universe is a strange one, being empty and never undergoing a Big Bang. Its value of q being negative (-q) denotes an accelerating Universe. But in working back towards time zero, its representative R(t) value never attains zero, which means that it has no beginning, i.e., has an infinite past. While theoretically interesting, the model defies most observational parameters, and the very notion of the Big Bang concept. The Steady State Universe was formulated by Hoyle and others as an "antidote" to the Big Bang model. It accepts expansion and implies that the Universe has no beginning or end. In order to preserve the matter density distribution determined for the Universe, the Steady State model requires a "creation field" in which new matter (mass) must be continuously created through time to balance the rate of expansion. Another model (not in above Table) also does not start with a Big Bang; this, the Eddington-Lemaitre model, is closed and finite and is static initially but thereafter starts expanding when the galaxies begin to form by Hydrogen gas condensation.

The Lemaitre model, derived from the Big Bang concepts, begins with a rapid increase in R during the early Universe but then experiences an extended period when R(t) remains nearly constant (owing to the effect of L being greater than Lc) so that expansion is minimal ("hovers") until much later resuming at an accelerated rate (read the modern version of this resumption of acceleration on the next page). The Abbe George Lemaitre (a Catholic priest from Belgium who also was a physicist) was the first to consider the starting state to be one of extremely high (approaching infinity) density (he called the singularity a "primeval atom"; later, George Gamow applied the Greek word "ylem" [primitive matter] to everything contained in such a singularity).

Among the three standard hot (high temperature) Big Bang models, the Open Universe model (also known as the Friedmann-Lemaitre model) predicts that expansion continues forever at an essentially constant rate through an infinite and unbounded space based on hyperbolic geometry (in which light can follow both positive and negative curvature simultaneously). Evidence so far suggests that a (nearly) flat Universe model, whose density is at the critical density (in which Ω = 1, the condition that there is just enough matter distributed throughout the Universe to cause it to expand forever even as it endlessly slows down) accounts for many of its observed properties, so that the Einstein-DeSitter Universe is currently the model most widely held to approximate reality. This model is in accord with current estimates for the age of the Universe.

The mental picture one gets from the word "Flat" as we have been applying it to cosmic expansion may be somewhat illusory. One meaning - just as the surface of a large balloon may appear flat to an ant at some point on it, so the Universe may in fact be spherical but acts as though flat within the region open to our direct observation (we experience this on Earth as our local surroundings appear flat out to the horizon but would show its real curvature if we were orbiting astronauts). However, flat on a Universe scale may mean just that - flat in our experiential Euclidian sense - imagine a table top that keeps expanding forever from within itself (not just by growth at the edges) in two primary directions; points at different parts of this infinitely growing top would all separate from each other. Table tops do have a third dimension (thickness), as presumably does a flat Universe, but expansion in that dimension may be finite.

Closed Universes follow spherical geometries. The prime model shows greater rates of expansion in early cosmic time with decreasing rates of augmentation thereafter. (This is not the same as the incredible but brief expansion almost at the very beginning of the Universe if inflation indeed is a real phenomenon.) Thus, the components of the Universe move outward powered in part by the inertia imparted by the energy release at the Big Bang. However, the mass/energy level is high enough for gravity to effectively pull on galaxies, stars, and other matter so as to gradually slow the expansion to a zero rate. Thereafter, the condition becomes one of increasing deceleration. The rate of separation between galaxies diminishes with time until, at some future time, expansion ceases and galaxies then draw closer at ever faster rates until all matter and radiation converge to a singularity (perhaps 50 b.y. in the future), undergoing what has been called the Big Crunch.

The Crunch concept remains intriguing. A group at Penn State University has carried out computer calculations that strive to combine General Relativity and Quantum Physics to derive a Quantum Gravitational model of a contracting Universe. This results in matter and energy in that previous Universe coming together in the singularity we know as the Big Bang. As contraction proceeds to its last moments, at its terminal stage quantum forces become repulsive, causing a quantum Big Bounce that seems similar in its properties to a Big Bang. Their model retains a consistency that does not rule out this possibility but the difficulty of trying to find confirmative evidence for this earlier Universe is only addressed in terms of the model being plausible without any direct proof.

This raises the possibility of Repeated Universes, as singularities explode, expand, ultimately contract to the next singularity, and then repeat the cycle indefinitely, or, even infinitely. However, this scenario seemingly would violate the entropy restriction in that the singularity should have a minimum rather than maximum state of disorder that is the outcome for every model. Multiple Universes (next page) that evolve simultaneously, or at different "times", are a possible consequence of the Chaotic Inflationary model which in recent years has gained favor as a variant of the inflationary version of the Big Bang. These Universes, however, have no likelihood of contact with one another, so that their existences may be unprovable.

To sum up this topic - the shape of the Universe. Evidence is building that the Flat condition is the most likely to describe this configuration. However, this "flatness" may be illusory: the Universe may be so large that what is viewed and perceived as "flat" is actually part of curved space - as viewed the curvature is too slight to be determined (imagine being on a small part of a very large balloon). Results from COBE and WMAP seem to offer solid support for the idea of real or apparent "flatness". Consider this diagram:

Theoretical distribution of departures from Cosmic Background Radiation uniformity, in terms of sizes of these deviations, for Flat, Open, and Closed Universes.

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.

Source: http://rst.gsfc.nasa.gov/