During these past fifty or so years, we have discovered our Universe and set it within the framework of the laws of physics. A concrete and coherent picture has emerged. This picture is indeed compel¬ling: there are few (if any) viable alternatives, and the theory has satisfied every test demanded of it. But is our confidence any more justified than, say, that of the Greeks hi their cosmologies, which were after all consistent with their view of the Universe? On the basis of historical precedent we might surmise that the theory will be continually altered to incorporate new data. This will happen either until the theory departs so far from the original concept that it can hardly be regarded as the same idea, or until so much additional structure is required to support the theory that it is no longer a simple theory. At that time a new view can easily displace the old theory. In this context we might think of the modifications to Newton’s theory of gravity that were introduced to account for t the slight anomaly in the motion of the planet Mercury. There were several ad hoc attempts to set matters right including the suggestion that the anomalies might be due to a planet whose orbit lay within that of Mercury. But it was not until the formulation of the General Theory of Relativity that a truly satisfactory answer to the problem was found. However, notwithstanding the radical change in viewpoint engendered by the theory of relativity, Newton’s law remains a very good description of what is going on. Similarly the Big Bang theory may be a good approximation to the state of affairs, even if some drastic conceptual innovations-should ultimately prove necessary.

In an attempt to stretch our theory of the Universe to its limits, we might well begin by trying to isolate those points at which our theory may encounter difficulty, or to ask questions which our theory may not be able to answer. In this way we build up a list of fundamental cosmological problems which are so often the subject of debate, and which lie on the ill-defined boundary between physics and metaphysics. Because these questions arise frequently we shall say something about a few of those which are questions of physics rather than philosophy.

Perhaps one of the central issues concerning the Big Bang cosmology is the issue of the cosmic singularity. If our ideas about the nature of matter are correct, and if in addition Einstein’s theory is the appropriate framework within which to discuss cosmology, the existence of a singularity hi our past is inevitable. A breakdown of the presently-accepted laws of physics is required in order to avoid the conclusion that our Universe evolved from a singular state. One such modification led to the Steady State theory, which is indeed singularity-free; however, we have seen that this theory is not consistent with the observational data. Indeed, if we invoke the nucleosynthesis arguments, we have good reason to suppose that any such changes in the laws of physics would only have been of importance during the first few seconds of the life of the Universe. Let us pursue this point a little further and ask- when might the laws of physics have been sufficiently different from the presently observed laws? We might well believe that matter exhibits peculiar properties when its densities exceed nuclear densities. There is no experimental information on this point, though it is not clear that any anomalous behaviour would necessarily have the required effect of removing the singularity. (The kind of anomalous behaviour we are looking for is, for example, the pressure of the cosmic medium becoming negative.) We have no reason to doubt the validity of general relativity in the kind of physical regimes observed so far, but as yet we have never studied a situation where the space-time curvature is very high. Ultimately, there comes a point when space-time can no longer be viewed classically and we should have a merger between general relativity and quantum theory. In the Universe, this would hap¬pen when the density is some 1090kilograms per litre! Even if it wore shown that the assumptions leading to a singularity break down at this point, it seems to be somewhat a matter of semantics as to whether we should say a singularity has been avoided!

If the Universe is closed, the force of gravity will eventually halt the expansion and cause the Universe to collapse towards another state of infinite density and temperature. This future singularity is as inevitable in a closed Universe as is the past singularity we have just been contemplating. A breakdown in the laws of physics in the vicinity of such a singularity might cause the Universe to bounce back and start another phase of expansion. In this way we arrive at the notion of an OSCILLATING UNIVERSE which has an infinite past and an infinite future. Classical thinking leads us to suspect that such a Universe might run down in much the same way as a bouncing ball eventually comes to a stop. However, such deductions can hardly take proper account of the all-important mechanism for the hypothetical bounce. The strongest argument against the oscillating Universe concept is that we do not appear to live in a closed Universe. If that is correct, then the cosmic singularity is a unique event.

We turn our attention now to a rather different problem which is rarely discussed in the popular literature on cosmology. It is one of the most important, as yet unanswered, questions: why is the Universe homogeneous and isotropic? A possible answer is “because it started off that way’, but as we shall see, this answer is inadequate and only sidesteps the central issue. Before going on to discuss this rather deep question, the reader may like to consider the following analogous phenomenon. A race is to be run with each of the competitors running in different neighbouring stadia. One starting-pistol is fired, and all the runners are seen to start simultaneously before any of them could have heard the report of the gun! If we observed such a scene, we would indeed be puzzled and wonder how the runners knew when to start. What we observe in the Universe is directly analogous. The homogeneity of the Universe implies that all parts must have commenced expanding in unison, and yet there is apparently no physical agency through which different regions could have communicated so as to synchronize their histories.

We can best illustrate the cosmological situation by reference to a space-time diagram . Consider two cosmic observatories A and B, and suppose that the Universe as observed from A and B is homogeneous and isotropic. Because the Universe expands, each of A and B will see more of it as time goes on. At sufficiently early times A and B will not be able to see each other, since the light rays emitted from A will not have had enough time to reach B, and vice versa. A and B are then said to lie beyond each other’s HORIZON. They are causally disconnected, by which we mean that at that time, nothing that has happened in the vicinity of A can affect B, and vice versa. At some later time, A receives the first signals from B. B is then said to have come within A’s horizon, and this is the first A knows of B’s existence. Subsequent to that time A and B can compare their respective environments, and eventually there comes a time when they realize that they have experienced almost identical cosmic histories. Although A and B could not communicate at very early times (and were even unaware of each other’s existence), the Universe somehow went bang simultaneously in both places. Thus our observation of the homogeneity and isotropy of the Universe on immense scales seems to imply some breakdown of the basic notion of CAUSALITY that the cause precedes the effect by at least as much time as it takes a light ray to travel from the point of cause to its point of effect. The feeling among some cosmologists is that this breakdown of causality must have occurred at or before the time when the picture of space-time as continuous breaks down. Needless to say, we are not yet sophisticated enough to cope with this problem theoretically: there has to date been relatively little success in merging the theory of relativity with quantum theory.

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