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

TL;DR

This paper proves the nonlinear future stability of spatially homogeneous FLRW solutions of the Einstein--massless Vlasov system with spatial topology ^3, showing their decay rates and comparing them to Minkowski space, for spherically symmetric perturbations.

Contribution

It establishes the nonlinear future stability of FLRW solutions with ^3 topology under spherically symmetric perturbations, including decay rate analysis.

Findings

FLRW solutions are nonlinearly stable to perturbations.

Decay rates of energy-momentum components are characterized.

Comparison of decay rates with Minkowski space is provided.

Abstract

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.