Small solutions of the Einstein-Boltzmann-scalar field system with Bianchi symmetry

TL;DR

This paper proves that small homogeneous solutions to the Einstein-Boltzmann-scalar field system with Bianchi symmetry exist globally and tend to de Sitter space, extending previous results to more general settings.

Contribution

It generalizes prior work by establishing global existence and asymptotic behavior for small solutions in Bianchi types I-VIII with scalar fields and matter.

Findings

Solutions exist globally in time for small initial data.

Solutions tend to de Sitter space asymptotically.

Results extend previous models with cosmological constant and flat FLRW spacetimes.

Abstract

We show that small homogeneous solutions to the Einstein-Boltzmann-scalar field system exist globally towards the future and tend to the de Sitter solution in a suitable sense. More specifically, we assume that the spacetime is of Bianchi type I--VIII, that the matter is described by Israel particles and that there exists a scalar field with a potential which has a positive lower bound. This represents a generalization of the work [19], where a cosmological constant was considered, and a generalization of [16], where a spatially flat FLRW spacetime was considered. We obtain the global existence and asymptotic behavior of classical solutions to the Einstein-Boltzmann-scalar field system for small initial data.