Future global existence and asymptotic behaviour of solutions to the Einstein–Boltzmann system with Bianchi I symmetry

Abstract

In this paper we study the Einstein–Boltzmann system with Bianchi I symmetry. We show that for small initial data the corresponding solutions of the Einstein–Boltzmann system are future geodesically complete and that they isotropize and have a dust-like behaviour at late times. Detailed information about the metric and the matter terms is obtained, and the results show that the solutions tend asymptotically to the Einstein–de Sitter solution.