The spatially homogeneous Boltzmann equation for massless particles in an FLRW background

TL;DR

This paper investigates the relativistic Boltzmann equation for massless particles in an expanding universe, proving the global existence of small solutions under certain conditions.

Contribution

It establishes the first global existence results for small solutions of the relativistic Boltzmann equation for massless particles in an FLRW background.

Findings

Global existence of small solutions in weighted $L^1\cap L^\infty$ space

Applicable to a range of soft and hard scattering potentials

Advances understanding of relativistic kinetic theory in cosmological settings

Abstract

We study the spatially homogeneous relativistic Boltzmann equation for massless particles in an FLRW background with scattering kernels in a certain range of soft and hard potentials. We obtain the future global existence of small solutions in a weighted $L^1\cap L^\infty$ space.