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This supplemental page presents ideas that describe a General Model for the SpaceTime expansion of the Universe following the first eras of the Big Bang. This and related subjects are considered in more detail on page 20-8, 20-9, and 20-10.

The model described below, using spheres to characterize expansion phenomena, is not necessarily the "correct" or "valid" depiction, as several space geometries are possible, each of which must also integrate time. We are using the "expanding sphere" concepts because this geometry is easy to visualize. In fact, most textbooks that cover Universe expansion rely on an "expanding balloon" analogy to help the student to grasp some of the properties of the enlargement of space. A balloon surface is a two-dimensional (2-D) topology whereas in fact space is three-dimentional spatially, with then the added attribute of time as another dimension (4-D).

We'll start with non-space (space is defined in the footnote at the bottom of page 20-1) or the "void" just before the sudden appearance of the singularity that leads to the Big Bang. A singularity comes into existence as a "real" entity (to ask where is meaningless since no geometric or dimensional parameters can be specified until space itself is created for this Universe by the expansion after the B.B.). At this instant, time begins for the Universe. The events described on page 20-1 (including Inflation) proceed through the Radiation Era. One can now imagine the Universe to have gone through a time-sequence of expansion in which the matter and energy components have moved ouward radially from the singularity as though they formed an expansion front that progresses as a growing "sphere on which the "explosion" products continuously reside. At any given time, this sphere, ever enlarging, is connected to the singularity not just by spatial dimensions (which are confined to the sphere) but by a time dimension, such that it serves as the lengthening radius of the sphere. The sphere - and the space it denotes - continues to grow (like a balloon inflating) up to the present time. Inside the sphere, there is nothing left from the Big Bang itself. However, we can imagine that there is a "nest" of smaller and smaller spheres within the present one, each representing the shape of the expanding Universe at its specified time at a stage of growth in the past.

Let us take a moment to examine this figure, which uses two inflated balloons to illustrate two aspects of space expansion.

The left balloon indicates the "size" of space (as a 2-D surface) at some time in the past. The right balloon shows a later time, such as the present. The yellow spots represent galaxies at each time. One can clearly see that the spots are farther apart in the later time case. They are in effect receding from one another. The wiggly blue lines in the left denote a light wave (sine wave type) whose wavelength lies in the visible blue. The red lines on the right denote waves with larger crest to crest distances, i.e., indicate a shift to a longer wavelength. This exemplifies what is known as the cosmic redshift (determined by examining the spectrum of radiation from galaxies: spectral lines move towards longer wavelengths as recessional velocities increase with distance towards the farthest galaxies; see page 20-9). (Note: the size of the yellow dots did not increase in the right sphere; this mirrors the observation that galaxies themselves undergo little or no expansion as space itself expands because their local gravity keeps their dimensions more or less constant and thus counteracts general space enlargement.

Thus, in this pictorial image which shows our model sphere at just two of a multiplicity of times, at any chosen time since the Big Bang there would be a sphere whose size is governed by the time radius. This sphere enlarges as time seems to move systematically from past to present. The physical entities occupying the Universe (stars, galaxies, dispersed matter and energy) all lie on the SpaceTime sphere (in some models a cone is used instead (see first part of this page) to help frame the growth of space for us earthlings who are conditioned to think in terms of Euclidian geometry but we will stick with the sphere for its ease in helping one to visualize what seems to be happening). At such different times the sphere always contains on its surface (which can be envisioned as having a finite thickness to represent the three dimensions of space) all that we would see, at each time, when looking out by telescope into the farthest reaches of the visible Universe. This limit to what we can observe is known as the "horizon" of the Universe.

We will now examine that spherical surface at two times: today (here assuming that the current best estimate for the Universe's history from the Big Bang onward has a starting time some 14 billion years ago), and at a time 5 billion years in the past.

First, the current time case. Arbitrarily, we choose some point on the sphere - designated as Earth. We look out through our best telescope - the Hubble Space Telescope - and see a succession of galaxies at different distances from Earth, with some being near the apparent edge of the Universe, some 13+ billion light years away. Others lie closer, at various distances as determined by converting their light year distances into the more familiar spatial parameters (e.g., kilometers). Remembering that we are visualizing these galaxies as lying on a very huge spherical surface, for convenience we choose to measure those distances by light-years. Galaxies close to our arbitrary point of observation are within a few billion light years and are spatially near the point. Those further away are farther apart from us on the sphere. At some light year distance we fail to see any more galaxies or other evidence of the matter/energy thrown from the singularity into a (hollow) spherical geometry defining a surface that has been expanding ever since. We have reached the horizon but we cannot say what, if anything lies beyond. It is generally agreed that the actual Universe is larger (by how much is still unknown) than the observable Universe. As time continues into the future objects (mainly galaxies) now beyond our ken will come into view progressively as the expansion front moves outward.

Another fact worth mentioning now is that theoretical models for expanding Universes consider the growth of space (at the expansion front) to occur at the speed of light. The outermost galaxies are moving the fastest (some nearing light speed) but those ever closer to us move at slower and slower relative speeds.

Now for the a strange peculiarity of this model, which is in fact a reality that was predicted by General Relativity. As our sightings from the Earth point extend further and further away on the sphere, we note that the galaxies - our principal objects to reference to in inventorying what we can detect at ever greater distances - appear to be less and less evolved. Astonishingly, the farthest ones we can resolve into shapes that indicate stages of evolution appear to be the youngest. (As a preview of what you will learn on pages 20-8 through 20-10, distances can be estimated fairly well out to about 4-5 billion light years by several techniques involving galaxy or exploding star luminosities). Working back closer and closer to Earth, we progressively pass and observe galaxies that appear older and older, until near Earth and its galaxy, the Milky Way, nearby galaxies seem to be in similar stages of development relative to our galaxy. This paradox is simply explained by assuming 1) that most galaxies started about the same time (1-2 billion years after the Big Bang); 2) that some galaxies are moving faster away at ever increasing velocities from us (as determined by the spatial-expansion mode of redshift [movement of specific wavelengths associated with spectral lines for elements like hydrogen towards progressively longer wavlengths]. with the farthest away having the largest shifts; 3), those now farthest from us have had their light or other types of radiation travel the longest (at an assumed constant light speed), so that, 4) their light left their vicinity at times in the earlier history of the Universe, when these distant galaxies were youthful, and 5) light waves from ever nearer galaxies haven't traveled as far and long, and hence were emitted later and later in their stages of evolution, and show systematic smaller redshifts.

The same general relationships would be found on a sphere with a radius of 5 billion light years (this is a time just before the Earth was formed). The farthest galaxies would still be moving the fastest and would appear the youngest. The closest would however be less evolved compared with now. The galaxies would be closer to each other (greater galaxy density) as space itself has been expanding for only 9 billion years.

So, in this conceptual model there are two roles played by time. First, it measures the "radius" at any given moment of the increasingly enlarging sphere. Second, it controls the observed age relationships (degrees of development) of galaxies in various positions on the sphere. The "lookback time" for any galaxy determines its distance from it to us, its cosmic age at the time we see it, and the (evolutionary) stage of its development

One interesting added notion: It doesn't matter where one is on the sphere - for example, if the galaxy-star-planet is billions of light years from our Milky Way, and intelligent beings analyze the Universe, they will see a Universe that has exactly the same behavior as described above. From this, we conclude that there is no spatial center of the Universe - observations from any point within it will lead to the same interpretations of its general properties. Moreover, this spherical model has the feature that there are no internal boundaries - one can start at any point on the sphere and move around it without ever transgressing some edge, and if proceeding in a single direction (but not a straight line since the sphere has curvature) the traveler will end up back at the starting point.

The shape of the Universe is very likely not that of a spherical surface that enlarges like a balloon. It may be flat (but with some depth) and is expanding its edges outward into the void. However, if the spherical Universe is very much larger than that part which is observable to us from Earth, its curvature for that region would be slight and would appear almost flat. Other expansion shapes, such as the double hyperbola, are possible, as depicted in this diagram:

The first is a closed Universe with a finite history of expansion that could end with a reduction in sphere radius back to a point (a new singularity); the other two would have a finite beginning but will expand infinitely over time and space; a Universe without a beginning or an end is a conceptual possibility but is not likely. (Note the property of the three triangles drawn on the surface of these geometric figures: for closed space, the sum of the angles is greater than 180°; for the open space hyperbolic case, the sum is less than 180°; for flat space, the sum is (as so familiar to us) exactly 180°.)

This diagram (oversimplified) shows the most favored three modes of expansion up until 1998. The circular slices denote a relative size of the observable Universe at various cosmic times.

Currently, most models for the Universe's growth lead to a flat geometry and open expansion. One property of a flat Universe is that it is so balanced that it neither collapses nor must expand forever.

In 1998, announcements were made of an astounding new set of observations that said, in effect, that the Universe, after the great inflationary burst in the a small fraction of the first minute after the B.B., apparently decelerated during perhaps the first half of its expansion history and then has since been accelerating (a cone diagram to represent this would be much like taking the second left figure as the bottom and then replacing the top part with something similar to the upper part of the figure on the right). The next diagram shows such a cone; it will be shown again on page 20-10.

The cause of this new pattern has been a form of repulsive energy (either much like Einstein's Cosmological Constant or "quintessence" or some other form of "dark energy") which is believed to comprise most of the energy of the Universe. Since the earliest history of expansion, gravity played a slowing role. But as the influence of gravity diminished with the expansion of space that progressively moved galaxies farther apart, thus weakening the slowing force, the repulsive energy became the stronger force leading to a resumption of acceleration after initial Inflation. These ideas are discussed in depth on pages 20-9 and 20-10.

Before we leave this special page extension, let me present one more important "mental picture" analogy that may aid in visualizing expansion. Remember, it is Space itself that is expanding: galaxies draw apart as they recede from any point of observation not because they were driven outward from an "explosion" of the singularity but because they appear to be part of a general, grossly homogeneous enlargement of the space geometry (whatever that proves to be), perhaps due to the above dark energy. To picture this, imaginative writers on Cosmology ask you to envision a tiny lump of bread dough (laden with yeast) that contains raisins scattered about. (There are several variants of this analogy). As the bread bakes, it rises uniformly. All the raisins remain in their initial relative positions but with the growing bread loaf they draw apart from each other. This may help you to envision the Universe's expansion - the big difference is that the bread will ultimately reach its final growth stage and has a finite boundary whereas the Universe may just keep expanding into an infinity of time and space.

As astronomers look out into the Universe from any place on Earth, the distances they measure to the (at the time) perceived limits (not edges) of the Universe will be the same, just as it would appear to be to other astronomers who might live on a planet in some distant galaxy. But, there is a conundrum to introduce here: the present day Universe is actually larger - perhaps 28 billion light years in size. To get an insight to this claim, link to this Web site sponsored by the Sloan Digital Sky Survey. It helps to crystallize the idea that the Universe is both mysterious and fascinating.

We can use this preceding paragraph to consider one last idea: It was stated several times in the first part of the page, and above, that the Universe we define as observable is almost certainly smaller than the actual Universe's size. From the above, it could well be at least 28 billion light years across. Now imagine you are located somewhere at a point within this larger Universe and you look out in several directions. You will see galaxies in various age/stages of their life spans. At any direction, if your telescope is capable of capturing photons usable as image makers of objects farthest away in spacetime (at the earliest moments after Recombination/Reionization), the age you determine will always be close to the 14 billion years currently acceptable as the best estimate of the start of Big Bang cosmic time. Now, imagine you move to some other place in the Universe. If you look out from there in any direction, the result will be the same as just described. But, if the first and second points are themselves more than 14 billion light years apart from each other, neither can now see the other. This is a consequence of horizon limitation.

Now if these two (inhabited) points were, say, 18 billion light years apart in the 28 billion light year Universe, it would be impossible for either to communicate with the other, since only 14 billion years are available for light speed travel. But what if there is also matter of some kind (not necessarily organized into galaxies) beyond the 14 billion light year observable horizon limit? If expansion could not be greater than light speed, there would seem to be an enigma in any attempt to explain this "beyond" matter and/or energy. Two possible (plausible>) explanations come immediately to mind. One, the "jump start" provided by Inflation might somehow be capable of extending the Universe into the unobserved. Two, at some stage (probably early) expansion may have exceeded the speed of light; several arguments (beyond the scope of this review) have been "dreamed up" (i.e., proposed but not proved) to define a physics that allows light speed to be greater than the current value. All this conjecture goes to show that there is still much to be learned in Cosmology.

We trust that this page will give you both a geometric and a temporal framework to refer to in succeeding pages. After you have explored more details by reading through pages 20-8, 20-9, and 20-10 (wait until you work through the intervening pages), come back to this page and see if it takes on improved meaning.

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