Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric

TL;DR

This paper investigates the behavior of certain cosmological models with collisionless matter, analyzing their dynamics near singularities and during expansion, highlighting differences from perfect fluid models and oscillatory behaviors in Bianchi type II models.

Contribution

It provides a detailed analysis of the dynamics of Einstein-Vlasov solutions with symmetry, comparing them to perfect fluid models and identifying asymptotic states.

Findings

Bianchi type II models exhibit oscillatory behavior near singularities.

The dynamics near singularities can be characterized and compared to perfect fluid models.

Some models show simpler oscillations than the mixmaster universe.

Abstract

The dynamics of a class of cosmological models with collisionless matter and four Killing vectors is studied in detail and compared with that of corresponding perfect fluid models. In many cases it is possible to identify asymptotic states of the spacetimes near the singularity or in a phase of unlimited expansion. Bianchi type II models show oscillatory behaviour near the initial singularity which is, however, simpler than that of the mixmaster model.