In this talk, we will consider the massless Boltzmann equation on FLRW spacetimes with spatial topology $\mathbb{T}^3$ in the linear and decelerated expanding regimes, where the scale factor is $t^{q}$ with $q\in (0,1]$. In these backgrounds, the massless Boltzmann equation admits a non-stationary Maxwell—Jüttner equilibrium that maximises the entropy of the system. In this work, we show this equilibrium is non-linearly stable for the massless Boltzmann equation on these spacetimes in the case of hard ball interaction. We will also discuss the non-linear stability of the vacuum when $q\in (1/3,1]$. This is joint work with Robert M. Strain (University of Pennsylvania) and Martin Taylor (Imperial College London).