Late-time behaviour of Israel particles in a FLRW spacetime with $\Lambda>0$

TL;DR

This paper analyzes the long-term behavior of Israel particles in a flat FLRW universe with positive cosmological constant, establishing global existence and asymptotics for solutions of the relativistic Boltzmann equation using energy methods.

Contribution

It provides the first analysis of the relativistic Boltzmann equation with a physically motivated scattering kernel in a cosmological setting, demonstrating global existence and asymptotic behavior.

Findings

Proves global-in-time existence of solutions.

Establishes asymptotic decay properties.

Applies energy method to relativistic Boltzmann equation.

Abstract

In this paper we study the relativistic Boltzmann equation in a spatially flat FLRW spacetime. We consider Israel particles, which are the relativistic counterpart of the Maxwellian particles, and obtain global-in-time existence and the asymptotic behaviour of solutions. The main argument of the paper is to use the energy method of Guo, and we observe that the method can be applied to study small solutions in a cosmological case. It is the first result of this type where a physically well-motivated scattering kernel is considered for the general relativistic Boltzmann equation.