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

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.