Once Before Time - Martin Bojowald [135]
A world model requires an understanding of the long-term behavior of the universe. It depends not only on quantum gravity in the big bang phase but also on parameters such as the matter content and the exact value of average spatial curvature. According to general relativity, these numbers determine whether an expanding universe can reach a point of maximal extension and then contract, or whether it must continue to expand for all eternity. Cosmologists tend to favor the first case—on the one hand, to avoid the dreadful idea of a universe ever more diluting, cooling, and thus increasingly dreary, but also because a cosmos initially contracting from infinite size, then rebounding once in a strong quantum phase, and finally forever expanding may be more difficult to explain. (But see the pre-Socratics for possible philosophical advantages of this apeiron picture.)
In a universe that is expanding, recollapsing, and rebounding time and again one has, with finitely long cycles in the infinity of time, more wiggle room to make preceding cycles responsible for the existence of the special conditions we find now. In the multitude of all cycles, very different and life-threatening conditions could often exist. But it suffices if in the infinite set of all cycles, every so often a part of a universe resembling ours can come about. As long as this is possible, with infinitely many attempts it is bound to happen; we would get rid of all need to explain why the universe is as we see it. However, Zeno’s ghost reappears once more, as infinity is abused to make the existence of a world like ours plausible. As an explanation for the world, this is hardly satisfactory.
For an example of a model crucially relying on the passage of many cycles, we can look at the so-called emergent universe, proposed by George Ellis and Roy Maartens in 2004,4 initially on a purely classical basis. According to the emergent model, the universe starts in a state resembling Einstein’s originally constructed static world model, but it differs slightly in some properties so that it is not entirely independent of time. In the emergent model, starting near the static universe, there is a series of cycles, all very short-lived. The model contains matter in such a form that some of its properties change slightly during each cycle, eventually assuming the negative pressure required for an inflationary phase. With inflation, the ensuing cycle can expand much more than its predecessors and thus in principle resemble the part of the universe visible to us now. And for some specific properties, certain constraints arise: The picture is in principle testable by comparison with observations.
There are a few problems with the classical model. For one, Ellis and Maartens must somehow avoid the singularities of general relativity, possible only by specialized constructions. Then, the static universe is unstable, making a start of the universe near this state very unlikely. It is like throwing a ball onto a corrugated surface such as an egg carton and asking where one would most likely find the ball. It would certainly not be on the elevated parts, which constitute unstable positions, but rather in the valleys. Even near a peak one would not be likely to find the ball, for it would soon roll down from there. The static Einstein universe, as a consequence of its instability, corresponds to a hill, and thus the original emergent model has severe difficulties in reliably explaining the precise initial condition it requires.
LOOP QUANTUM COSMOLOGY: COMING FULL CIRCLE
Interestingly, both problems are elegantly solved by a combination with loop quantum cosmology, as George Ellis has shown with David Mulryne, Jim Lidsey, and Reza Tavakol.5 Singularities are avoided in any case by quantum repulsive forces, easily providing a cyclic model. But independently—and more surprisingly, if one already knows the singularity avoidance—a new static universe, of much smaller size than Einstein’s, arises; and this one is stable. It is an ideal