Asymptotic behaviour of the relativistic Boltzmann equation in the Robertson-Walker spacetime

TL;DR

This paper investigates the long-term behavior of solutions to the relativistic Boltzmann equation in an expanding universe model, establishing global existence and analyzing how cosmic expansion influences matter distribution evolution.

Contribution

It proves global existence of classical solutions for certain scattering kernels and studies their asymptotic behavior in the context of Robertson-Walker spacetime.

Findings

Global existence of solutions established

Asymptotic behavior of matter distribution analyzed

Expansion of universe impacts matter evolution

Abstract

In this paper, we study the relativistic Boltzmann equation in the spatially flat Robertson-Walker spacetime. For a certain class of scattering kernels, global existence of classical solutions is proved. We use the standard method of Illner and Shinbrot for the global existence and apply the splitting technique of Guo and Strain for the regularity of solutions. The main interest of this paper is to study the evolution of matter distribution, rather than the evolution of spacetime. We obtain the asymptotic behaviour of solutions and will understand how the expansion of the universe affects the evolution of matter distribution.