I. Introduction - II. Our knowledge on the physical universe. 1. The size and age of the universe. 2. The evolution of the universe. 3. The matter in the universe: Stars, Galaxies and Dark Matter. 4. The matter and radiation in the universe: the background radiation. - III. The dynamics of the first stages of the universe: the inflation - IV. Key Obsevations of contemporary cosmology. 1. The background radiation and the indication of a “Big Bang”. 2. The primordial abundances of the light chemical elements. 3. The systematic redshifts of distant galaxies and the expansion of the universe. - V. The assumptions of contemporary cosmology and the models of universe. 1. The conceptual presupposition of cosmology. 2. The standard Friedmann-Lemaître-Robertson-Walker (FLRW) models. - VI. The questions on the origin and the future of the universe. 1. Is the Big Bang the origin of the universe? 2. Science, philosophy and theology on the destiny of the universe. 3. Further theological reflections on cosmology.
The word “cosmology” has become more and more frequent in scientific literature. It designates the area of physics and astronomy which investigates the observable universe as a single object of study, its history, its structure, its dynamics and the processes which are or have been important in its evolution. Some specialists would also include the origin and the destiny of the universe in the subject matter of cosmology - and to a limited extent these are issues for the cosmologist. However, as we shall see, the ultimate destiny of the universe — and, even more so, its ultimate origin — can not really be adequately treated by cosmology as such.
This article will discuss the basic understanding contemporary scientific or physical cosmology has of the observable universe — of its history beginning with the Big Bang and of its structure and the key processes which have fashioned, or are fashioning, its evolution — and the issues which it directly raises in dialogue with theology. It is important to note that there are two other meanings of the term “cosmology,” which are related to, but also very different from, physical cosmology. “Cosmology” has also been used to designate the philosophical treatment of the material world — of time and space, of change, of place, etc. — philosophy of nature. We should really call this “philosophical cosmology”. The questions it tries to answer require input from the natural sciences, including physics, astronomy and physical cosmology, but its methods and scope go beyond those of scientific cosmology to consider both the presuppositions of the natural sciences and the philosophical conclusions based on their findings.
A third meaning of “cosmology” is found within the studies of cultures — cultural anthropology. In this context, a “cosmology” is a coherent collection of stories, images, rituals, explanations in a culture or society which describe in an imaginative way the origin of the world, of human kind, of natural phenomena, of social institutions, etc. These mythic elements endow cultural and social institutions and events — indeed the life of the cultural and society itself — with meaning and significance. They provide the basis for ethical and social behavior — and for understanding the ultimate meaning of life (cf. Bolle, 1987). The remainder of this article will focus on physical, or scientific, cosmology, and on its relationships with issues in the theology of creation.
Fundamentally, physical cosmology, (which I shall hereafter refer to simply as “cosmology”), using physics and mathematics, constructs a detailed model of the observable universe, on the basis of evidence gathered from astronomical observations and physics experiments. As more and more information concerning the history, structure and behavior of the universe becomes available, the model undergoes modifications, additions and fine-tuning. What does cosmology tell us about the universe now as we move into the third millennium?
II. Our knowledge on the physical universe
1. The Size and Age of the Universe. The universe is incredibly vast. To appreciate how vast it is, it is helpful to recall that our own Galaxy, the Milky Way, is about 100,000 light years in diameter and consists of about 100 billion stars, of which our Sun is just one. There are at least 100 billion other galaxies in the observable universe. And the most distant objects we are detecting, quasars and primordial galaxies, are of the order of 10 billion light years away — the light we are receiving from them now was emitted that long ago. Thus, the observable universe is between about 13.7 billion light years in radius, in terms of the time it has taken light from the most distant parts of the universe we now see to reach us. However, in the meantime, the universe has expanded a great deal. So those most distant observable regions are now at least of the order of 40 billion light years from us, but we cannot see them as they are now - only as they were just after the Big Bang.
Thus, we can see that the universe is very old, about 13.7 billion years since the Big Bang. To relate that to the history of the Earth and the Solar System, it is helpful to note that a very firm figure for the Earth's age — from geological evidence — is 4.6 billion years. Now, in saying that the observable universe is, say, 15 billion years old, counting from the Big Bang we should not consider the Big Bang as the absolute beginning of everything. Cosmology cannot determine that — it is very possible, even likely, that physical reality in some completely quantized configuration existed “before” the Big Bang, even though time as we know it may not have (see below, VI.1).
2. The Evolution of the Universe. One of the most important characteristics of the universe as we now understand it is that it is expanding and cooling. Therefore it is also evolving. It was much, much different at various stages in the past than it is now. Right after the Big Bang, it was extremely hot and dense, with a temperature above 1032 °K — so hot and dense, in fact, that the laws of physics themselves were very, very different, as was the physical reality they would have described. The four fundamental interactions of physics — gravitation, electromagnetism, and the strong and weak nuclear interactions — were almost certainly unified into one single “superforce”. It was too hot for there to be space and time as we know them, or any of the particles and structures we recognize now. Then, as the universe expanded and gradually cooled, at various threshold temperatures the fundamental interactions successively split apart, and new things became possible. Eventually — still much less than a second after the Big Bang — the temperature of the universe was cool enough for particles like protons, neutrons and electrons to form. However, it was not until much, much later that stars formed — only after more than several tens of millions of years after the Big Bang. And it is only with stars that we first have the manufacture of the heavy elements — all the elements heavier than helium and lithium. Thus, complex molecules, like those which constitute the bulk of earthly reality around us, and our own bodies, were only possible after the first generation of stars had died and spread the heavy elements they had produced throughout their neighborhoods. Thus, cosmological evolution is the essential precursor to the emergence of life, and the processes of biological evolution.
Very generally the evolution of the cosmos can be described as the gradual development from being very hot to being very cold, from being very, very dense to being nearly empty, from being very smooth to being very lumpy, from being very simple (just a vast expanding ball of hot ionized gas) to being very complex (composed of many systems of superclusters, and clusters, of galaxies, each of which is full of clusters of stars), from being undifferentiated to being very highly differentiated. And this complexity and differentiation is even more impressive on microscopic scales — with the development of the 92 natural elements, and all the vast array of molecules they are capable of forming, including DNA and proteins, which carry the information that is essential for the emergence, development and maintenance of life and consciousness.
3. The Matter in the Universe: Stars, Galaxies and Dark Matter. Another significant feature of our universe is its density — on average it is 10-31to 10-29grams per cubic centimeter at the present time. (Obviously, the farther back into the past one goes, the higher the density he or she encounters.) It is empty — but not quite, fortunately for us! In turns out that this density is very close to the critical density — that needed to insure that the present expansion will eventually come to a halt, to be followed by collapse. Recent data indicate that this density is probably less that critical, and even that the expansion of the universe may be slightly accelerating. This would mean that the universe would expand forever. The acceleration of the expansion would indicate that something like vacuum energy — the energy of space empty of particles, but not of fields! — is presently dominating the dynamics of the universe. Such vacuum energy (which is often referred to as “the cosmological constant” L, first introduced, but then rejected, by Einstein) can generate a repulsive negative-pressure gravitational force.
Even before the resurgence of L, cosmologists and astronomers realized that less than 5% of all mass/energy in the universe is luminous. 95% of it is dark, and we know about it only through its gravitational influences. With the recent realization that expansion seems to be accelerating, there is a cautious consensus that much of this dark mass/energy — about 73 % of the total mass/energy of the universe — is something like vacuum energy, or possibly some other form of dark energy. Of the remaining 27 %, which is almost certainly matter, most it — 22 % or 23 % of the total — is dark matter, and cannot be baryonic — cannot be composed of protons and neutrons, furthermore, it is also clear that most of this dark matter cannot be baryonic, like all the matter we are made of, and are familiar with. We know practically nothing else about this overwhelmingly dominant nonbaryonic matter — it could be in the form of massive neutrinos, axions, gravitinos, neutralinos, or other similar pervasive but very elusive and difficult to detect weakly interacting massive particles (WIMPS).
How is this matter in our universe distributed? Obviously, the luminous matter is presently distributed in very lumpy fashion on all small and intermediate length scales. We see planets and stars, clusters of stars, and these in turn are grouped into galaxies, with most of the galaxies being found in clusters — with large expanses of almost empty space, filled with some dust and gas, between them. These clusters of galaxies are usually part of very large filamentary structures called superclusters, which encompass voids, areas relatively empty of galaxies, of the order of 100 million light years or so across. This is what is sometimes referred to as the “soap bubble structure” of the universe. There is considerable evidence that at least some of the nonbaryonic mass/energy is also distributed in lumpy fashion — in a way which underlies and perhaps induces or supports the lumpiness of the luminous matter.
4. The Matter and Radiation in the Universe: the Background Radiation. But, despite this hierarchical lumpiness on so many scales, the matter of the universe seems to be distributed very smoothly on the very largest scales — on scales larger than about 500 million light years. If we look out into the universe in different directions, its texture is similar everywhere — the same type and roughly the same degree of galactic clustering. Finally, and most importantly, there is the cosmic microwave background radiation (CMWBR) at 2.73 °K, which we see at almost this same temperature in every direction on the sky. It is the “afterglow” of the Big Bang — the primeval fireball as we see it now. The CMWBR originates from the expanding hot, almost homogeneously distributed gas about 300,000 years after the Big Bang when its temperature had cooled to about 4,000 °K. At this temperature the free electrons in the plasma recombine with protons to form neutral hydrogen atoms, and the universe for the first time becomes transparent to radiation. This is long before the universe became lumpy — in fact, it is only after this time that structure can begin to form, as perturbations in the gas — slight overdensities — begin to grow and later collapse to form galaxies and clusters of galaxies. Thus, the CMWBR we detect is coming from the cosmic plasma long before stars and galaxies existed. The smoothness of this CMWBR reflects the very smooth distribution of matter at that time, which in turn indicates that on some very large scale at the present time the distribution of matter in the universe is on average still very smooth, and looks the same in all directions. Looking at the universe is like looking at colored construction paper under a microscope, and then looking at it from far away — on a bulletin board. Under the microscope, it is looks very lumpy — composed of splotches of blue, red, or green. However, that lumpy microscopic structure melts into a very smooth colored expanse when seen from a distance — when our eye automatically averages the color over larger volumes. The observable universe is the same way.
Thus, as we peer out into space in every direction — with microwave eyes — between all the galaxies, our line of sight eventually encounters the fogbank, at which the universe becomes opaque to radiation. This is at an observed distance of about 13.7 billion light years from us, in terms of the time it has taken those microwaves to reach us — just 300,000 light years shy of the Big Bang itself. (It should be remembered that as we see farther out into space, we are also seeing farther back in time — this is simply due to the finite velocity of light. Thus, the photons we are receiving right now in the CMWBR are carrying information directly to us concerning the conditions of the cosmic plasma when the universe was just about 300,000 years old and only an expanding ball of smoothly distributed hot gas — before there were ever any stars or galaxies, as mentioned above.) It is from this fogbank, or what is technically referred to as the last scattering surface, that the microwave photons constituting the CMWBR emanate. This radiation has what is known as a blackbody, or equilibrium, spectrum. That indicates that the matter and radiation in the universe were in complete equilibrium at that time, and in epochs much earlier than that. Furthermore, as already mentioned briefly, the fact that the black body temperature of this CMWBR is very smooth — varies only by one part in a 100,000 over the whole sky, once peculiar velocity effects are neglected — indicates that the density of matter at that time varies only by one part in 100,000, too. Temperature variations code for density fluctuations.
However, these tiny density fluctuations in the primeval plasma, which were first confirmed through the positive detection of fluctuations (anisotropies) in the CMWBR blackbody temperature by the Cosmic Background Explorer (COBE) satellite in 1992, are very significant. They are considered to be the seeds of later galaxy formation. Without them, there would be nothing from which galaxies, clusters and superclusters of galaxies, and therefore stars, could evolve. If the density of the universe is perfectly smooth, then it remains perfectly smooth, unless some mechanism generates density fluctuations. But, if there are already slight overdensities and underdensities in the primordial cosmic material at some point, whatever their origin, then as the universe expands these overdensities and underdensities can grow to form the rich astronomical structure we now behold.
The way this happens is very simple — it is due to gravity. Consider cosmic overdensities. Because there is slightly more matter in the overdensity, there will be a slightly stronger gravitational attractive force tending to draw that overdense region together. Due to this that region will expand less rapidly than the surrounding universe. Thus, its density will increase further, and its expansion rate will decrease even further. Eventually, the overdensity, or perturbation as it is often called, will reach a point where it stops expanding altogether and begins to collapse under its own weight (gravity again!). As it collapses it will fragment into thousands or even millions of knots, each of which themselves will collapse, forming a cluster of stars or galaxies, depending on how big the original cloud of gas was to begin with. And, as these regions and sub-regions collapse, they will begin to spin faster and faster, due to the conservation of angular momentum (just as a figure skater spins faster and faster as she draws her arms closer to her body). Thus, the overdensities discovered by COBE in the primordial cosmic plasma are essential to our understanding of how our universe came to be the way it is today.
III. The dynamics of the first stages of the universe: the inflation
However, this raises a more fundamental question: Where did these overdensities and underdensities — these perturbations — come from? How can they be explained? We need to account for them. At the same time, there is another very puzzling coincidence which needs explanation. This is what is called “the horizon problem.” If we look out into the universe in different directions all the way to the last scattering surface and ask how large causally self-connected regions on that surface are (that is, regions which are small enough, so that different points within them could have shared information — which cannot travel faster than the speed of light — with one another during the 300,000 years since the Big Bang), we find that the largest such causally self- connected regions will be only about one degree across on the sky! — if the universe was expanding at a “normal” rate since the Big Bang itself. Thus, the last scattering surface we see, from which the CMWBR originates, is, from this point of view, tiled with about 50,000 little regions which are causally isolated from one another. But, if they are causally isolated from one another, how then can we explain how the temperature of the material in them is practically the same, as indicated by the CMWBR measurements?! This is a very serious problem!
It turns out that both of these problems — the origin of perturbations and the horizon problem, as well as a host of other similar problems — can be solved, if we postulate a very early period of super-rapid, exponential expansion, referred to as “inflation”. If for a very brief interval, of the order of “illionths” of second, the universe expanded by at least 30 orders of magnitude — that is, by a factor of 10-30 — then both of these serious enigmas disappear. In the first place, it happens that inflationary expansion generates a spectrum of perturbations in a well-defined way and freezes them into the primeval plasma until such a time that they can begin to grow, after the matter in the universe decouples from the radiation. Secondly, if inflation occurred, then the ancestral region from which our observable universe originated was much, much smaller just after the Big Bang than it would have been without inflation. This simply means that with inflation the part of the universe from which our observable universe originated was causally self-connected beforehand, and therefore remained causally self-connected thereafter, eliminating the horizon problem. (It can be demonstrated that, once a region is causally self-connected, it will remain so throughout an inflationary period.) Thus, practically all cosmologists today postulate that there was such an inflationary period shortly after the Big Bang, which then ended before the universe was 10-30 seconds old. There is as yet no direct confirmation that such an inflationary period actually occurred. However, at the same time, there is no evidence that is inconsistent with such an epoch, and, what is most important, there is so far no other viable alternative for solving both the perturbation and the horizon problems.
Inflation is closely related to the vacuum energy we discussed earlier (see above, II.3) — the presence of Λ, the cosmological constant. The only way in which we can imagine inflation occurring is by the driving force of a positive vacuum energy, which can be shown to induce exponential expansion. It is relatively easy to see where such a vacuum energy might be generated in the very early universe. Two strong possibilities are: 1.) right at the transition from the fully quantized configuration in what is called the Planck era, when physics is completely dominated by the superforce we mentioned above, to the universe with space, time and gravity as we know them now (if space is still 3-dimensional at those extremely high energies instead of, say 10 dimensional, then this happened when the temperature slipped below 1032 °K, and gravity separated from the superforce, leaving the combined nongravitational interactions united in a single Grand Unified Theory (GUT) force. These in turn broke apart at somewhat lower temperatures.); and 2.) a little later, when the temperature of the expanding universe sank beneath 1027 °K, and the strong nuclear interaction separated from the electroweak interaction (the unification of the electromagnetic force and the weak nuclear force), thus inducing a great deal of vacuum energy in this phase transition. In both cases it is fairly easy to account for the generation of dominant vacuum energy in small, causally connected regions of space, which under its influence would then undergo extremely rapid expansion — inflation.
At the same time, however, the universe must be able to exit from this rapidly expanding state, and in this exit it must somehow be reheated (the exponential expansion is accompanied by supercooling!) up to some fairly high temperature as it resumes normal expansion and cooling. This can be accomplished by having the vacuum energy rapidly dissipate into heat and particles. But this should not happen too rapidly! Before that occurs the universe has to expand enough to solve the horizon problem, and also to generate the perturbation spectrum. Providing a completely satisfactory model for the inflation mechanism is a very difficult, but probably not impossible, task, and has not yet be accomplished. Besides enabling enough expansion and adequately explaining reheating, the scalar field which is usually invoked to provide the vacuum energy to drive inflation, must also be consistent with demands of particle physics and lead to density perturbations of the observed amplitude at the time of last scattering, when the finishing touches on the CMWBR were made. Finally, the inflationary period which results must also lead to a density of matter in the universe which is consistent with the one we presently observe. It was until recently commonly held that inflationary periods inevitably lead to a universe with a density extremely close to the “critical density” (that just above which its expansion would eventually halt). If this were so, and if the density turns out to be less than critical, as is still possible, inflation would be ruled out. However, it has now been established that certain types of inflationary scenarios do not necessarily lead to a nearly critical-density universe.
Thus, it seems that, though an inflationary epoch is quite difficult to incorporate consistently into an adequate overall cosmological model of our observable universe and the physics which governs it, it is still both possible and promising. Of course, as already mentioned, it is very important to find ways of determining whether or not inflation did occur, particularly positive evidence for it. If it turns out that inflation could not have happened, then cosmologists will be very much in the dark as to how very important features of the universe — the nearly constant CMWBR temperature in all directions and the galactic and stellar structure we see — are ultimately to be explained. No other reasonable alternative to inflation has appeared on the horizon.
IV. Key Obsevations of contemporary cosmology
1. The background radiation and the indication of a “Big Bang.” Having discussed in some detail what we know of the universe, it is time to focus on what evidence we have for saying all this. In the course of what has already been presented, we have seen that the CMWBR provides the strongest evidence for the principal characteristics of the universe as we know it. It is the observational cornerstone of cosmology. Let us now summarize what the CMWBR tells us, and may eventually tell us.
The CMWBR has been, and is being, very thoroughly studied and measured with increasing precision on many different angular scales. Its very existence as cosmic background radiation is the strongest evidence we have that there was something like the Big Bang — it assures us that there was a time when the temperature of the universe as a whole was more than 4,000 °K (it is now 2.73 °K, the present temperature of the CMWBR). Thus, together with other corroborating evidence, it compellingly indicates that, as we go back farther and farther into the past with our observations, we encounter a succession of ever hotter, ever denser phases. The theoretical limit of these, from the simple, standard models we use (Friedmann-Lemaître-Robertson-Walker (FLRW) models, which are both isotropic and spatially homogeneous — that is, both spherically symmetric and containing matter and pressure which are constant at any given time; see below), is what we call the “Big Bang.” According to these, the temperature and the density of the universe becomes infinite at the Big Bang. Cosmologists usually assign this Big Bang or initial singularity the time t = 0. We shall discuss the Big Bang and what it means more thoroughly below. Strictly speaking the Big Bang itself lies beyond the limits where the models are reliable — they are adequate until a temperature of 1032 °K (if there are 3 spatial dimensions in those extreme conditions; more spatial dimensions decreases this transition temperature). Beyond that point, the physics upon which the models depend — in particular, Einstein's theory of gravity and of space-time — breaks down. In order to investigate what really happens at those enormous temperatures, a quantum theory of gravity has to be used. As yet we do not possess a satisfactory one, though superstring theories look very promising (see, for example, Greene, 1999).
The next most important feature of the universe and its history the CMWBR convincingly demonstrates is that there was a time when all the matter in the universe was nearly homogeneous (smooth) — when there were no stars or galaxies. Along with this is the nearly incontrovertible evidence that at even earlier times the matter in the universe was ionized, in perfect equilibrium with the radiation it contains. Therefore the matter was coupled to (by electron scattering), and opaque to, that radiation. As already mentioned above, the almost featureless smoothness of the density at the time the CMWBR was last scattered further indicates that there must be a presently very large length scale on which the average density is constant — that the universe is almost spatially homogeneous on that scale.
Finally, the slight perturbations, or fluctuations, of the blackbody temperature of the CMWBR — as already indicated — signal the presence of similarly slight fluctuations in the matter density at that time, providing evidence for the beginning of the formation of structure in the universe. These temperature fluctuations are presently being extensively studied on all scales, and their varying amplitudes and the patterns of their varying amplitudes tightly constrain our models of the universe and the processes important in its evolution. For instance, the preliminary indication that these perturbations are scale-invariant — that their strength does not depend on their size — is at least consistent with their origin in a very early inflationary episode. And the placement and strength of the fluctuations on a scale of about 1 degree, which are due to acoustic oscillations (sound waves) in the ionized gas at last scattering, helps us constrain the mass-energy density and the baryon density — of the universe — and indirectly the amount of dark matter and dark energy.
2. The primordial abundances of the light chemical elements. Moving from the CMWBR, another key piece of evidence in cosmology is the abundances of helium, deuterium and lithium. Let us concentrate on helium and deuterium here. The abundance of helium in the universe is about 24% by weight. But stellar processes can account for very little of that. And deuterium, which is a fragile isotope of hydrogen (with a proton and neutron in the hydrogen nucleus, instead of just a proton), cannot be manufactured by stars, only destroyed. So where did all the helium and the significant trace of deuterium come from? According to our knowledge of nuclear physics and what our simplest adequate cosmological models indicate, conditions (temperature, density, and neutron-proton ratio) between 1 and 3 minutes after the Big Bang, when the temperature was between 1011 and 109 °K, were just right for forming lots of helium (in fact, just about 24% by weight!) and some deuterium and lithium. After the temperature sinks below about 109 °K, the production of these elements ceases and their abundances are frozen into the cosmic gas. All the heavier elements, like carbon, oxygen, phosphorous, copper, iron, chlorine, uranium, etc., are only produced later — in the cores of stars or in the supernova explosions which herald their demise.
The primordial abundances of helium and deuterium give further very compelling evidence then that there was a time when the temperature of the universe was at 1011 °K. They add weight to our simple picture of the universe — the Big Bang picture — expanding, cooling and evolving from a very dense, very hot initial state. They also strongly support the detailed but very simple FLRW models of that early stage of the universe, together with the equilibrium thermodynamics and nuclear physics we employ to describe the matter and its interactions then. Finally, it is important to mention that even more careful and detailed measurements and interpretations of this primordial abundance data, including that of lithium, give strong evidence that only a very small percentage of the matter in the universe can be baryonic. Most of it must be nonbaryonic, as we mentioned before. Unfortunately, those data cannot by themselves constrain what sorts of nonbaryonic particles constitute that dominant component. That remains one of the great mysteries of physics and cosmology!
3. The systematic redshifts of distant galaxies and the expansion of the universe. Finally, there is the first really key cosmologically significant observation that was made — by E. Hubble and M. Humason — the systematic redshifts of distant galaxies, which indicate that the universe is indeed expanding. The farther away a galaxy is from us, the more its light is redshifted. These redshifts can be precisely measured by determining at what wavelengths recognizable lines (of hydrogen or of nitrogen, say) in galaxies’ spectra are found. Then a given redshift is simply the factor by which an observed wavelength has shifted from that line's “rest wavelength.” Since these redshifts were first detected, astronomers have exerted great efforts to obtain the redshifts of galaxies and quasars to great distances. This redshift mapping has not only confirmed the expansion of the universe and of the galaxies with it, but has also provided, together with improved independent distance measurements, determinations of the Hubble parameter, the rate at which the universe is expanding, and detailed evidence of the large scale clustering of galaxies — “the soap-bubble structure” of the universe, to which we referred earlier (see above, II.3).
It should be emphasized here that the expansion of the universe we are talking about is not the movement of the galaxies and quasars away from us within the space that surrounds them and us, but rather the expansion of space itself. The galaxies remain relatively fixed in space — though they move a little bit within space, by what is referred to a their “peculiar motions.” Space, like a three-dimensional balloon, is expanding, and carrying the galaxies with it! During inflation, as we have seen, this expansion of space is exponentially rapid. It can thus involve the separation of galaxies from one another at many times the speed of light. This is all right — since Einstein's special relativity only forbids massive particles moving through space more rapidly than the velocity of light. It does not say anything about how rapidly space itself may expand or inflate.
In considering the three key categories of observations in cosmology — the CMWBR, the primordial abundances of helium, deuterium and lithium, and the systematic redshifts of distant galaxies — we should immediately notice that they are independent of one another and strikingly support the same general conclusions — that the universe is both expanding and cooling, and that the farther we go back into the past, the hotter and denser it was. There are also other cosmologically significant observations, such as the degree of clustering in the universe — the strength of clustering between galaxies and between clusters of galaxies on different scales. This turns out to be a very important piece of information, as it constrains models of galaxy formation and sifts out some possible nonbaryonic dark matter candidates. Galaxy number counts with distance is another general type of observation, which can help us determine the density of baryonic matter, as well as the intrinsic (non-cosmological) evolution of galaxy populations. (One of the great problems in observational cosmology is separating out the effects of these intrinsic evolutionary processes from those of the expanding, cooling universe itself). Even somewhat pervasive and obvious characteristics of the universe and its behavior — such as the overwhelming dominance of matter over anti-matter and the one-way direction time assumes (time only goes forward, not backward — this is often referred to as “the arrow of time” problem) — require explanation in cosmology or in the physics associated with it. Both of these problems will probably only find answers in investigations of the very early universe, in the details of the processes which dominated the Planck epoch, or the extremely short period just afterwards — around the time when inflation may have occurred.
Before moving on, it is helpful to ask: “Is there such a thing as the observable universe as a single object, which is the principal focus of cosmology?” Or is there, instead of “a universe,” just a collection of disparate objects — galaxies and clusters of galaxies — having very different histories and therefore essentially unrelated to one another? From what we have just seen, there is strong evidence that it does indeed make sense to consider the universe as a single object of study. In particular the existence and character of the CMWBR demonstrates that all that we can presently see in the universe — to the very limits of our technological reach — has a common history, and is intimately interconnected. Further confirmation of this is found in the common universal physical and chemical laws, which seem to hold throughout the universe, and in the common large-scale features which we see in every direction. The universe does give overwhelming evidence of being a single connected manifold or complex. This is one of contributions of contemporary cosmology.
V. The assumptions of contemporary cosmology and the models of universe
Now we turn to consider very briefly the models cosmologists and physicists construct to describe the universe, and to make predictions about how it should behave at times, temperatures and densities which are not directly accessible to our observational capabilities. But first, we shall discuss the assumptions which they make in developing these models.
1. The conceptual presupposition of cosmology. Like any science, cosmology begins with a number of assumptions, which neither it nor any other science as such can completely justify. Some of these assumptions are explicitly articulated. Others are not. Among those which are not usually expressed are several very basic ones which we must make in order to begin any investigation. These are: that something “out there” exists, rather than nothing; that effects require causes; that physical reality is ordered and not entirely chaotic. The justification for these assumptions is fundamentally that “they work” — they enable us to get somewhere and are pervasively supported by our pre-scientific experience and knowledge.
There is also one assumption of a more philosophical tenor which cosmologists often explicitly mention. It is that the same physical laws hold uniformly throughout the universe. The laws of gravitation and of electromagnetism, for example, which we can demonstrate hold here in the immediate neighborhood of the Earth and the Solar System, are assumed to hold in exactly the same way throughout the universe. There is some scientific justification for this — from careful astronomical observations we have some evidence — but not enough evidence — that the laws of atomic physics, for instance, and of electromagnetism and gravity are same in the vicinity of a distant quasar as on earth. These observations give some indication that matter behaves the same way there as it does here.
And now we need to discuss two assumptions which are proper to cosmology and which are always mentioned. The first of these is “the cosmological principle” and the second is “the manifold-metric model of space-time.”
The cosmological principle simply states that there are no physically privileged spatial points or locations in the universe. In particular, our position within the universe is in no way physically privileged — the universe therefore should look very much the same from any other location at this time in its history. Strictly applied this assumption implies that the universe is isotropic (spherically symmetric) and spatially homogeneous (smooth — not lumpy — that is, spherically symmetric about every point!).
But the universe is not spatially homogeneous! It is lumpy on all small and intermediate length scales. This implies that the cosmological principle cannot hold precisely in its exact or strong form. The fact that we are intelligent observers, for instance, implies that we must be have a moderately overdense, very temperate and stable — and therefore somewhat privileged — location! At the same time, we would want to assert that observers on planets in any other galaxy would detect the same CMWBR, the same systematic redshifts of distant galaxies, the same primordial abundance of elements, and see the same overall structural texture.
Turning to the manifold-metric model of space-time, this simply means that space-time is treated as a continuous four-dimensional membrane — or a continuous three-dimensional surface which expands or contracts smoothly in time. On the membrane or manifold is a metric, or “distance function,” which expresses the distance from one point to another and which also describes angles. Modeling space-time this way automatically endows it with certain properties, which it may or may not have in reality. For instance, we speak of the spatial manifold or membrane expanding at certain rate, like a balloon, and possessing a certain vacuum energy. The question is: does this not imply that space-time is already a container or an object in too absolute a sense? At the same time, however, it seems eminently reasonable to use this model, because it incorporates the spatial and temporal relations objects and events possess relative to one another.
Finally, there are two physical assumptions which cosmologists always make. The first is the assumption of a theory of gravity — almost always Einstein's general relativity, which has Newton's gravitational theory as its classical limit. Without a theory of gravity you cannot have cosmology, only a cosmography. Gravity gives a cosmological model its dynamics and its evolutionary characteristics. It specifies how a given spatial configuration at one time will evolve into spatial configurations at later times under the influence of the mass-energy distributed within it. Or, going backward in time, the gravitational theory tells us what antecedent spatial configurations must have been like, given a particular spatial configuration now.
The second physical assumption is the fluid approximation for the matter and the radiation content of the universe. Essentially this means that both are distributed in such a way that a well-defined density can be assigned at each point and that a relationship between density, pressure and temperature holds (given by a so-called “equation of state”). One needs such an equation of state, or its equivalent, to determine uniquely a cosmological model. If the fluid approximation does not hold — if, for instance, matter turns out to be hierarchically clustered on all length scales — that is, if there is no very large length scale above which matter becomes smoothly distributed on average (as preponderant evidence now indicates) — then the fluid approximation would be invalid. In that case we would have to use the very unwieldy techniques of what is called kinetic theory to describe the mass-energy distribution in the universe.
2. The Standard Friedmann-Lemaître-Robertson-Walker (FLRW) Models. Although we have already mentioned the very important standard FLRW cosmological models in our extensive discussions so far (see above, IV.1), it is time to focus our attention on them very briefly. We want to describe them, comment on their usefulness and adequacy, indicate what they help to tell us about the universe and its origin and destiny, and describe how we typically use them as the basis for dealing with structure formation.
The FLRW models which form the standard theoretical foundation of cosmology are really just the spherically symmetric (isotropic) and spatially homogeneous solutions to Einstein's field equations with a perfect fluid equation of state. These solutions describe spherically symmetric space-times filled with matter which has a constant density at any given time — that is, it is without any lumps or spatial variations. These space-times are intrinsically dynamic. They represent three-dimensional spaces either expanding or contracting, with expanding universes cooling and contracting universes heating up. There are three classes of FLRW models: a) those which have enough matter in them (the density of matter is greater than the critical density) so that they expand to a maximum radius, and then collapse; b) those which have just exactly the critical density, and thus have flat three-dimensional space-sections and just manage to continue to expand forever; and c) those which have a mass-energy density which is below the critical density, or which, though having a 2 density equal to or above critical density, have negative-pressure dark energy (such vacuum energy - a positive cosmological constant) dominating regular matter, and thus will expand forever. Having the critical density — in the absence of dark energy — means that the gravitational forces induced by it.
As already indicated, a very important feature of FLRW models is that they possess an initial singularity, or Big Bang. If we go back in time from any point in an FLRW model, we find that in some finite period in the past, the universe so described encounters a singularity — a point at which the density, temperature, and curvature of the universe goes infinite. This is almost always interpreted as representing the “initial state,” or origin, of the universe and is conventionally assigned the time t = 0. It is obvious, too, that these models also indicate two general possibilities for the final state of the universe, depending on whether or not the density of mass-energy in the universe is greater than the critical density (cf. Clark, 1997; Adams and Laughlin, 1997). If the density is just critical or less than critical, the universe will expand forever, gradually running down and dispersing to the point that no further star formation, galaxy formation or any other local regenerative processes will occur. The universe would no longer be life-bearing. This is what is called cosmological “heat death.” If, on the other hand, the density of the universe is greater than the critical density, the gravitational force due to the matter in the universe will eventually bring the expansion to a halt and induce collapse. In its accelerating contraction the cosmos would get hotter and hotter as it plunges back towards some extremely hot and dense state similar to what it was like near the Big Bang. This would obviously also completely destroy all the complex structures it had produced. Below we shall discuss more fully what philosophical and theological significance should be attributed to this cosmic “origin” and “destiny” as given by these standard FLRW models.
But first we need to evaluate briefly the significance of the FLRW models within the overall context of contemporary cosmology. How important are these very simple, standard models in giving us an overall general picture of what the universe is really like? The fact that the universe is lumpy on all small and intermediate scales may lead us believe that these FLRW models, which are exactly isotropic and spatially homogeneous, really do not even approach adequacy in describing the universe as it really is and should not be trusted. But this would be a seriously flawed conclusion. Though the FLRW models as such cannot describe these inhomogeneities and their behavior, they do describe very well the large scale features of the cosmos and its thermal history amazingly well. All of the key observational evidence, the systematic redshifts of distant galaxies, the abundances of the elements, the various stages the universe as whole has negotiated since the Big Bang, and most importantly the cosmic microwave background radiation, strongly substantiate the picture provided by these models.
Furthermore, although inflationary epochs as such cannot be explained by what is given by an FLRW model as such (considerations beyond those involved with such models are needed), they and the processes leading to them can be easily incorporated and described within the FLRW framework — via a dominant cosmological constant, or vacuum energy. Of course, at very early times and at extremely high temperatures, immediately after the Big Bang, FLRW models are completely inadequate, as already indicated and as will be briefly revisited — quantum gravity effects will dominate and a much more fundamental quantum treatment of this region is needed. However, once the universe has emerged from this era (the so-called \Planck era"), cooling to less than 1032 °K, FLRW models provide a remarkably accurate description of the evolution and general features of our cosmos. Finally, even with respect to structure formation itself, which exact FLRW models cannot describe, thorough mathematical-physical treatments based on FLRW models — what are called “linearized perturbed FLRW models” — seem to provide very good approximations to the beginning and initial development of structure formation on most scales. This is essentially because, from the anisotropies in the CMWBR, we know that structure formation began from very small deviations from the background FLRW matter density of the universe. The growth of such deviations is easily described by linearized perturbation theory, based on the FLRW background. Only later stages of the evolution of such structure — the final collapse of perturbations to form stars and galaxies — require nonlinear treatment.
VI. The questions on the origin and the future of the universe
1. Is the Big Bang the origin of the universe? From what we have already seen, the answer to this question has to be “no.” There are several reasons for this important conclusion. First, although the initial singularity given by the FLRW models can be considered “the origin of the model universe” they describe, we have already emphasized that those models break down precisely in the region near the singularity. Very different physics — involving quantum gravity, the possible unification of gravity with the three nongravitational physical interactions and the application of these to the very early universe — is needed to describe this crucial initial phase of the universe's history in any way even approaching adequacy. The promising preliminary work being done in this area of quantum cosmology seems to indicate, for instance, that practically all schemes for treating this cosmic regime require the “disappearance of time” as we know it: time is something that only gradually emerges from the quantum configuration of the early universe as it makes the transition into the space-time manifold described by Einstein's gravitational theory, general relativity (cf. Isham, 1988, 1993). Thus, strictly speaking, it is only an analysis of an adequate quantum description of this very early phase of the universe which could possibly shed light on its “origin”. That would have to include some consideration of the fact that, since time as we know it disappears as we go backwards into this initial quantum state, there may not have been an origin of the universe in time, but only an origin of time from some pre-existing, “timeless” quantum state.
Secondly, given our present understanding of the limitations of the physical sciences, in particular of physics and cosmology, it is clear that neither can ever really indicate or model the ultimate origin of the universe, how it makes the transition from complete and utter nonexistence — from absolutely nothing — to existence, and how the laws which govern its behavior ultimately arose. Cosmology, along with the other sciences, always presuppose existence and order. They are incapable of ultimately explaining it. Finally, the question of the ultimate origin of the universe then is not a question of a beginning in time, which as we now see may not even be indicated from a quantum cosmological point of view, but rather the question of the ultimate ground of the universe’s being and order, which must transcend the universe itself, since it is contigent — it does not contain the ultimate explanation of its own existence. Quantum cosmological schemes, like those of Hawking and Hartle, Vilenkin, and Linde, which suggest possible processes by which the universe as we know it emerged from a vacuum state, or from some other very simple quantum configuration are interesting, provocative and important educated suggestions as to how the universe became as it is, but they should not be confused, as they sometimes are, with providing an ultimate explanation of the cosmos and of physical reality cf. Isham, 1988; Zycinski, 1996).
2. Science, philosophy and theology on the destiny of the universe. Similarly, the destiny of the universe as predicted by our cosmological models should not be taken as indicating that there is no personal afterlife, or that theological or philosophical intimations of immortality are purely illusory. From what we know of cosmology, it is true that practically any elaboration or improvement of our understanding of physical and cosmological futures leads inevitably to either something like heat death or to a fiery big crunch. However, it must be remembered that in constructing physical theories and cosmologies, many aspects of reality have been abstracted from, in order to focus on the purely physical and cosmological in their simplest terms. Certainly the ultimate death and dissolution that is evident from these considerations, and from many others in astronomy, biology and neurophysiology, is strongly confirmed by experience. However, at the same time there are powerful indications involving universal personal, ethical, aesthetic and religious experiences which reveal, or at least indicate, a positive ultimate destiny which is hidden at the core of, but transcends, limited and seemingly ill-fated reality. The details of how that is related to and emerges from our own death and dissolution and that of the universe takes us beyond where sciences can go.
3. Further theological reflections on cosmology. From what we have just seen, we can appreciate that the Big Bang should not be considered “the creation event,” the beginning of all that exists outside of God in time. We may still consider it as a symbol of “the creation event” as long as we do not identify it as such. That is, it is a scientifically based expression of the contingency of the universe and of all reality as we know and experience it. However, theologically speaking, creation, in its most radical meaning, does not imply ultimate temporal origination — although that may be very well be involved — but rather ultimate dependence on something, that is on the divine, which is capable of accounting for ultimate existence and order. Strictly speaking, as St. Thomas Aquinas well appreciated, it is possible that material reality existed from all eternity in some form or other and is still utterly dependent on God — that it is still very much God's creation (cf. Summa theologiae, I, q. 46, a. 2; De Aeternitae mundi).
Scientific cosmology: F.C. ADAMS, G. LAUGHLIN, “A Dying Universe: The Long-Term Fate and Evolution of Astrophysical Objects,” Review of Modern Physics 69 (1997), pp. 337-372; S. CLARK, Towards the Edge of the Universe (New York: Wiley & Sons, 1997); G. ELLIS, “Major Themes in the Relation between Philosophy and Cosmology,” Memorie della Società Astronomica Italiana 62 (1991), pp. 553-605; B. GAL-OR, Cosmology, Physics and Philosophy (New York: Springer, 1981); B. GREENE, The Elegant Universe (New York: Norton & Co., 1999); G. LEMAITRE, L'Hypothèse de l'atome primitif. Essai de cosmogonie (Paris: Dunod, 1946); C.J. ISHAM, “Creation of the Universe as a Quantum Process,” in Physics, Philosophy and Theology: A Common Quest for Understanding, R. RUSSELL, W. Stoeger, G. Coyne, eds. (Vatican City State: Vatican Observatory, 1988), pp. 375-408; C.J. Isham, “Quantum Theories of the Creation of the Universe,” in Quantum Cosmology and the Laws of Nature, R. RUSSELL, N. MURPHY, C. ISHAM, eds. (Vatican City State - Berkeley, CA: Vatican Observatory and The Center for Theology and the Natural Sciences, 1993), pp. 49-89.
Historical, philosophical and interdisciplinary aspects: J. BARROW, Theories of everything. The quest for ultimate explanation (Oxford: Clarendon Press, 1990); K.W. BOLLE, “Myth: An Overview,” in The Encyclopedia of Religion, M. ELIADE, ed. in chief, Vol. 10 (New York: Macmillan Co., 1987), pp. 261f; cf. also K.W. BOLLE, “Cosmology: An Overview,” in ibidem, Vol. 4, pp. 100-107; W.L. CRAIG, Q. SMITH, Theism, Atheism and Big Bang Cosmology (Oxford: Clarendon Press, 1993); S. JAKIi, Science and Creation (Edinburgh: Scottish Academic Press, 1974); E.L. MASCALL, Christian Theology and Natural Science (London: Longmans, 1956); E. MCMULLIN, “How Should Cosmology Relate to Theology?,” in The Sciences and Theology in the Twentieth Century, A. PEACOCKE ed. (Notre Dame, IN: University of Notre Dame Press, 1981), pp. 17-57; J. MERLEAU-PONTY, The Rebirth of Cosmology (Athens, OH: Ohio University Press, 1982); J. MERLEAU-PONTY, La cosmologie, le point de vue du philosophe, in “La cosmologie moderne”, H. ANDRILLAT et al., eds. (Paris: Masson, 1984), pp. 9-37; E.A. MILINE, Modern Cosmology and the Christian Idea of God (Oxford: Oxford University Press, 1952); J. POLKINGHORNE, M. WELKER (eds.), The End of the World and the Ends of God (New York: Trinity Press International, 2000); G. SMOOTH, Wrinkles in time (London: Little, Brown & Co., 1993); H.J. VAN TILL, “Basil, Augustine, and the Doctrine of Creation's Functional Integrity,” Science and Christian Belief 8 (1996), pp. 21-38; H.J. VAN TILL, “The Creation: Intelligently Designed or Optimally Equipped,” Theology Today 55 (1999), pp. 344-364; W. YOURGRAN, A.D. BREACK (ed.), Cosmology, History and Theology (New York: Plenum Press, 1977); N.M. WILDIERS, The Theologian and his Universe. Theology and Cosmology from the Middle Ages to the Present (New York: The Seabury Press, 1982); J. ZYCINSKI, “Metaphysics and Epistemology in Stephen Hawking's Theory of the Creation of the Universe,” Zygon 31 (1996), pp. 269-284.