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

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.