Isotropization of Slowly Expanding Spacetimes

We show that the homogeneous, massless Einstein-Vlasov system with toroidal spatial topology and diagonal Bianchi type I symmetry for initial data close to isotropic data isotropizes towards the future and in particular asymptotes to a radiative Einstein-deSitter model. We use an energy method to obtain quantitative estimates on the rate of isotropization in this class of models.