Isotropization of solutions of the Einstein-Vlasov system with Bianchi V symmetry

TL;DR

This paper proves the future stability and isotropization of solutions to the Einstein-Vlasov system with Bianchi V symmetry, showing they tend to the Milne universe, and highlights the instability of the flat Friedmann solution.

Contribution

It extends stability analysis to Bianchi V models, demonstrating asymptotic stability and isotropization in Einstein-Vlasov solutions, a novel application of methods from Bianchi class A models.

Findings

Solutions are asymptotically stable to the Milne universe.

Spatially flat Friedmann solutions are unstable within this class.

Expanding models tend to the Milne solution over time.

Abstract

Using the methods developed for different Bianchi class A cosmological models we treat the simplest Bianchi class B model, namely Bianchi type V. The future non-linear stability for solutions of the Einstein-Vlasov system is demonstrated and it is shown that these solutions are asymptotically stable to the Milne solution. Within the isotropic solutions of the Einstein-Vlasov system the spatially flat Friedmann solution is unstable within this class, and expanding models tend also to the Milne solution.