Bianchi I solutions of the Einstein-Boltzmann system with a positive cosmological constant

In this paper we study the future global existence and late-time behaviour of the Einstein-Boltzmann system with Bianchi I symmetry and a positive cosmological constant $\Lambda>0$. For the Boltzmann equation we consider the scattering kernel of Israel particles which are the relativistic counterpart of Maxwellian particles. Under a smallness assumption on initial data in a suitable norm we show that solutions exist globally in time and isotropize at late times.