The Einstein-Vlasov System with a Scalar Field

Abstract.We study the Einstein-Vlasov system coupled to a nonlinear scalar field with a nonnegative potential in locally spatially homogeneous space-time, as an expanding cosmological model. It is shown that solutions of this system exist globally in time. When the potential of the scalar field is of an exponential form, the cosmological model corresponds to accelerated expansion. The Einstein-Vlasov system coupled to a nonlinear scalar field whose potential is of an exponential form shows the causal geodesic completeness of the space-time towards the future. The asymptotic behavior of solutions of this system in the future time is analyzed in various aspects, which shows power-law expansion.Communicated by Sergiu Klainerman