Asymptotic behaviour of the Boltzmann equation as a cosmological model

TL;DR

This paper studies the long-term behavior of solutions to a modified Boltzmann equation modeling an expanding universe, revealing how cosmic expansion influences particle dynamics.

Contribution

It derives a modified Boltzmann equation for cosmological models and analyzes its asymptotic behavior in the soft potential case, connecting kinetic theory with cosmology.

Findings

Asymptotic behavior depends on universe expansion rate

Derived a stability condition for the modified Boltzmann equation

Identified decay rates of solutions in the soft potential case

Abstract

As a Newtonian cosmological model the Vlasov-Poisson-Boltzmann system is considered, and a slightly modified Boltzmann equation, which describes the stability of an expanding universe, is derived. Asymptotic behaviour of solutions turns out to depend on the expansion of the universe, and in this paper we consider the soft potential case and will obtain asymptotic behaviour.