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

## TL;DR

This paper proves that solutions to the Einstein-Boltzmann system with Bianchi I symmetry and a positive cosmological constant exist globally and become isotropic over time, under small initial data assumptions.

## Contribution

It establishes the global existence and late-time isotropization of solutions for the Einstein-Boltzmann system with Bianchi I symmetry and Israel particle scattering kernel.

## Key findings

- Solutions exist globally in time.
- Solutions isotropize at late times.
- Results hold under small initial data assumptions.

## Abstract

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.