The Einstein-Vlasov-Scalar Field System with Gowdy or T2 Symmetry in Contracting Direction

Abstract

We prove in the case of cosmological models for the Einstein-Vlasov-scalar field system with Gowdy symmetry, that the solutions exist globally in the past. The sources of the equations are generated by a distribution function and a scalar field, subject to the Vlasov and the wave equations respectively. The result is generalized for the case of T2 symmetry. Using previous results, we deduce geodesic completeness.