The Friedmann--Lemaitre--Robertson--Walker family of spacetimes are the standard homogenous isotropic cosmological models in general relativity. Each member of this family describes a torus, evolving from a big bang singularity and expanding indefinitely to the future, with expansion rate encoded by a suitable scale factor. I will discuss a mixing effect which occurs for the Vlasov equation on these spacetimes when the expansion rate is suitably slow. This is joint work with Renato Velozo Ruiz (Imperial College London).