Compact hyperbolic universe and singularities

TL;DR

This paper investigates the geometric and causal properties of compact hyperbolic universes, showing they inevitably contain singularities and discussing implications for cosmic censorship and universe models.

Contribution

It demonstrates that compact hyperbolic universes cannot have smooth time-slices and must contain singularities, extending previous results to inhomogeneous models and relating to cosmic censorship.

Findings

Compact hyperbolic universes cannot have smooth compact time-slices.

Universal covering space can be extended beyond the Cauchy horizon but contains dense singularities.

Results relate to ergodicity and the strong cosmic censorship conjecture.

Abstract

Recently many people have discussed the possibility that the universe is hyperbolic and was in an inflationary phase in the early stage. Under these assumptions, it is shown that the universe cannot have compact hyperbolic time-slices. Though the universal covering space of the universe has a past Cauchy horizon and can be extended analytically beyond it, the extended region has densely many points which correspond to singularities of the compact universe. The result is essentially attributed to the ergodicity of the geodesic flow on a compact negatively curved manifold. Validity of the result is also discussed in the case of inhomogeneous universe. Relationship with the strong cosmic censorship conjecture is also discussed.