Late-time behaviour of the Einstein-Boltzmann system with a positive cosmological constant

TL;DR

This paper analyzes the long-term evolution of the Einstein-Boltzmann system with a positive cosmological constant, demonstrating convergence to de Sitter space for certain homogeneous models.

Contribution

It establishes future global existence and asymptotic behavior of solutions for the Einstein-Boltzmann system in Bianchi types excluding IX.

Findings

Solutions converge to de Sitter space at late times

Global existence of solutions for Bianchi types except IX

Asymptotic behavior characterized by exponential expansion

Abstract

In this paper we study the Einstein-Boltzmann system for Israel particles with a positive cosmological constant. We consider spatially homogeneous solutions of Bianchi types except IX and obtain future global existence and asymptotic behaviour of solutions to the Einstein-Boltzmann system. The result shows that the solutions converge to the de Sitter solution at late times.