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Spatially homogeneous FLRW solutions constitute an infinite dimensionalfamily of explicit solutions of the Einstein--massless Vlasov system withvanishing cosmological constant. Each member expands towards the future at adecelerated rate. These solutions are shown to be nonlinearly future stable tocompactly supported spherically symmetric perturbations, in the case that thespatial topology is that of $\mathbb{R}^3$. The decay rates of the energymomentum tensor components, with respect to an appropriately normalised doublenull frame, are compared to those around Minkowski space. When measured withrespect to their respective $t$ coordinates, certain components decay fasteraround Minkowski space, while others decay faster around FLRW.

Future stability of expanding spatially homogeneous FLRW solutions of  the spherically symmetric Einstein--massless Vlasov system with spatial  topology $\mathbb{R}^3$