Future attractors of Bianchi types II and V cosmologies with massless Vlasov matter

TL;DR

This paper demonstrates that specific cosmological solutions act as attractors in Bianchi types II and V universes with massless Vlasov matter, using energy methods to analyze decay rates of perturbations.

Contribution

It establishes the attractor nature of Collins--Stewart and Milne solutions in Bianchi II and V models with massless Vlasov matter, employing novel energy and bootstrap techniques.

Findings

Generalized Collins--Stewart solution attracts Bianchi II models

Milne solution attracts Bianchi V models

Decay rates of perturbations are explicitly determined

Abstract

It is shown that the generalized Collins--Stewart radiation and Milne solutions are attractors of the massless Einstein--Vlasov system for Bianchi types II and V spacetimes, respectively. The proof is based on an energy method and bootstrap argument which are used to determine the decay rates of the perturbations away from the attractors.