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

TL;DR

This paper investigates the evolution of certain cosmological models governed by Einstein-Vlasov equations, revealing that massive particle solutions tend to resemble massless or dust solutions at different cosmic times.

Contribution

It provides a detailed analysis of the asymptotic behavior of Einstein-Vlasov solutions in Bianchi models with massive particles, extending understanding of their long-term dynamics.

Findings

Massive particle solutions are asymptotic to massless solutions at early times.

Solutions with massive particles approach dust solutions at late times in Bianchi I and II.

Bianchi type III models are also consistent with dust asymptotics at late times.

Abstract

The dynamics of the Einstein-Vlasov equations for a class of cosmological models with four Killing vectors is discussed in the case of massive particles. It is shown that in all models analysed the solutions with massive particles are asymptotic to solutions with massless particles at early times. It is also shown that in Bianchi types I and II the solutions with massive particles are asymptotic to dust solutions at late times. That Bianchi type III models are also asymptotic to dust solutions at late times is consistent with our results but is not established by them.