  Spatially homogeneous FLRW solutions constitute an infinite dimensional
family of explicit solutions of the Einstein--massless Vlasov system with
vanishing cosmological constant. Each member expands towards the future at a
decelerated rate. These solutions are shown to be nonlinearly future stable to
compactly supported spherically symmetric perturbations, in the case that the
spatial topology is that of $\mathbb{R}^3$. The decay rates of the energy
momentum tensor components, with respect to an appropriately normalised double
null frame, are compared to those around Minkowski space. When measured with
respect to their respective $t$ coordinates, certain components decay faster
around Minkowski space, while others decay faster around FLRW.
