In this talk, we will consider the Vlasov equation on expanding isotropic homogeneous tori described by the Friedmann–Lemaître–Robertson–Walker cosmological spacetimes. For expansion rate $t^q$, with $0 < q \leq 1/2$ (excluding some exceptional values), we show that the difference of a time-normalised spatial density with the spatial average decays with a quantitative rate depending on the regularity of the initial datum.