Global solutions of the Vlasov-Poisson-Boltzmann system in a cosmological setting

In this paper, the Vlasov-Poisson-Boltzmann system is studied in the context of Newtonian cosmology. An explicit background solution which describes the evolution of our universe is constructed, and global existence of homogeneous solutions that are perturbations around the background solution is obtained. Depending on the rate of expansion of the universe it is observed that the solutions have different behaviours at a large time. At a slow rate of expansion the solutions tend to an equilibrium state, but it turns out that such a slow rate is not physically well-motivated. At a rapid rate of expansion it is showed that the solutions behave like solutions of the Vlasov equation.