Cosmic Censorship for Some Spatially Homogeneous Cosmological Models

TL;DR

This paper investigates the global behavior of certain spatially homogeneous cosmological models with collisionless matter, proving that no finite-time singularities occur under specific conditions and establishing strong cosmic censorship for key symmetry classes.

Contribution

It demonstrates the absence of finite-time singularities in these models and proves strong cosmic censorship for Bianchi I, Bianchi IX, and Kantowski-Sachs classes.

Findings

No singularity occurs if mean curvature remains finite.

Strong cosmic censorship is proved for Bianchi I, Bianchi IX, and Kantowski-Sachs models.

Models with finite mean curvature avoid finite proper time singularities.

Abstract

The global properties of spatially homogeneous cosmological models with collisionless matter are studied. It is shown that as long as the mean curvature of the hypersurfaces of homogeneity remains finite no singularity can occur in finite proper time as measured by observers whose worldlines are orthogonal to these hypersurfaces. Strong cosmic censorship is then proved for the Bianchi I, Bianchi IX and Kantowski-Sachs symmetry classes.