Global Properties of Locally Spatially Homogeneous Cosmological Models with Matter

TL;DR

This paper investigates the singularity structure of locally spatially homogeneous cosmological models with matter, showing that expanding phases are singularity-free under certain conditions, while contracting phases always end in singularities.

Contribution

It provides a comprehensive analysis of singularities in Einstein-matter solutions, including perfect fluids and collisionless matter, under reasonable assumptions.

Findings

No singularities in expanding phases under certain matter conditions

Contracting phases always end in curvature singularities

Includes analysis of various matter models like perfect fluids and collisionless matter

Abstract

The existence and nature of singularities in locally spatially homogeneous solutions of the Einstein equations coupled to various phenomenological matter models is investigated. It is shown that, under certain reasonable assumptions on the matter, there are no singularities in an expanding phase of the evolution and that unless the spacetime is empty a contracting phase always ends in a singularity where at least one scalar invariant of the curvature diverges uniformly. The class of matter models treated includes perfect fluids, mixtures of non-interacting perfect fluids and collisionless matter.