Annu. Rev. Astron. Astrophys. 1984. 22: 157-184 Copyright © 1984 by Annual Reviews. All rights reserved

6. CONCLUSION

If we assume the standard FLRW geometries, then different equations of state or field equations resulting in sufficiently large effective energy violation imply the possibility that there is no singularity at the beginning of the present phase of expansion of the Universe. This expansion could start from a stationary state (either a static phase or an exponentially expanding phase) or could be a bounce from a previous collapse. Any "bounce" that occurs must have taken place at very early times, if our present picture of the origin of the microwave background radiation and the elements is correct. It is plausible that quantum field effects could cause a bounce at extremely early times, but the foundations of quantum cosmology need clarification before such a statement is on firm footing; if this does not happen, the quantum field effects probably at least make the singularity less severe (e.g. by eliminating particle horizons).

A different geometry implies the possibility of quite different kinds of singularity, which entail different concepts of creation. Finite density singularities can occur at the beginning of the Universe in the case of tilted homogeneous cosmologies, lessening the severity of the initial singularity. (One must haye some real singularity at any "beginning" of the Universe, for otherwise we can continue the Universe past this event to earlier times, thus showing that it was a "fictitious" singularity rather than a real one.) A major difference in the case of inhomogeneous universes is the possibility of timelike singularities, which continue to interact with the Universe over a period of time - perhaps for the entire history of the Universe - rather than the once-and-for-all interaction of the singularity in the standard theory, where creation takes place at one time and then the singularity is only an incident in the past.

There are two kinds of steady-state universe that seem to have the potential of giving a reasonable description of the astrophysical evidence: the original steady-state universe of Bondi, Gold, and Hoyle; and the two-centered static universe of Ellis, Maartens, and Nel. In both cases creation is a continuously proceeding process - in the first case diffused through space and in the second localized at a singular center of the Universe. However, both of these models run into difficulties when compared in detail with observational evidence.

The next major possibility is that the Universe started off in a steady-state situation and then changed to an evolutionary phase, as in the Eddington-Lemaitre expansion from an Einstein static state or the Starobinski expansion from a de Sitter steady-state phase; there may also be suitable models expanding from an Ellis-Maartens-Nel static phase. A major problem with any such stationary-state origin is how the Universe chooses when to break this phase and start the present evolutionary phase: "Since the initial metric has a finite life-time, it could not exist as t - , and therefore some other metric should exist before it" (53).

If a bounce takes place, it either comes from a state that has existed for indefinitely long in the past, perhaps collapsing from an infinite radius; or else it is a rebounce following a previous state of expansion from a state of high density, as in the "phoenix" universes that perpetually oscillate, and in many ways give an attractive understanding of the history of the Universe (20, 58). Each rebirth can take place either through effective energy violation or quantum effects (when no singularity occurs) or through the occurrence of isolated singularities that are sidestepped by most of the matter and that interact with the Universe for a brief period.

A singularity will exist unless effective energy violation takes place; it will provide an initial boundary to the Universe as we know it. The singularity could be "weak," so that quantum mechanically one can follow the Universe through to the era preceding the initial singularity; that is, one may be able to provide a theory of creation. Any such theory of creation of the Universe must by necessity postulate some preexistent structure that provides the basis for the equations used to describe creation (e.g. a previously existing oscillating universe, Minkowski space, a de Sitter universe, superspace, or pregeometry). These issues cannot be pursued further here; we refer the reader to the Appendix of Linde's (53) paper and the references therein.

There are then a variety of possibilities available, both within standard general relativity (where a variety of geometries are considered) and in variations of that theory, for understanding the nature of the origin of the Universe. The SHBB is one of this family but is by no means the only conceivable member; further possibilities are not completely excluded experimentally or theoretically.