Past stability of FLRW solutions to the Einstein-Euler-scalar field equations and their big bang singularites

TL;DR

This paper proves the nonlinear stability of FLRW solutions to Einstein-Euler-scalar field equations in higher dimensions, demonstrating their evolution towards Kasner-like singularities with curvature blow-up.

Contribution

It establishes the nonlinear stability of FLRW solutions with specific sound speeds and describes the nature of resulting big bang singularities in higher-dimensional spacetimes.

Findings

FLRW solutions are nonlinearly stable in contracting directions

Perturbed solutions evolve towards Kasner-like singularities

Singularities exhibit curvature blow-up and AVTD behavior

Abstract

We establish, in spacetime dimensions $n\geq 3$, the nonlinear stability in the contracting direction of Friedmann-Lema\^itre-Robertson-Walker (FLRW) solutions to the Einstein-Euler-scalar field equations with linear equations of state $P=c_s^2 \rho$ for sounds speeds $c_s$ satisfying $1/(n-1)<c_s^2 < 1$. We further show that nonlinear perturbations of the FLRW solutions are asymptotically pointwise Kasner and terminate in crushing, asymptotically velocity term dominated (AVTD) big bang singularities characterised by curvature blow-up.