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

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.