Open and Closed Universes, Initial Singularities and Inflation

TL;DR

This paper proves the existence of initial singularities in expanding universes without relying on the timelike convergence condition, extending previous results to include many closed universes and implications for inflationary models.

Contribution

It establishes initial singularity theorems applicable to both open and many closed universes without assuming the timelike convergence condition, which is violated in inflation.

Findings

Initial singularities exist in expanding universes without the timelike convergence condition.

The theorem extends to many closed universes, not just open ones.

Implications for gravitational collapse and inflationary cosmology.

Abstract

The existence of initial singularities in expanding universes is proved without assuming the timelike convergence condition. The assumptions made in the proof are ones likely to hold both in open universes and in many closed ones. (It is further argued that at least some of the expanding closed universes that do not obey a key assumption of the theorem will have initial singularities on other grounds.) The result is significant for two reasons: (a)~previous closed-universe singularity theorems have assumed the timelike convergence condition, and (b)~the timelike convergence condition is known to be violated in inflationary spacetimes. An immediate consequence of this theorem is that a recent result on initial singularities in open, future-eternal, inflating spacetimes may now be extended to include many closed universes. Also, as a fringe benefit, the time-reverse of the theorem may be applied to gravitational collapse.