  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.
