Past instability of FLRW solutions of the Einstein-Euler-scalar field equations for linear equations of state $p=K\rho$ with $0 \leq K<1/3$

TL;DR

This paper uses numerical methods to study the stability of FLRW solutions in Einstein-Euler-scalar field equations with linear equations of state in the contracting universe, confirming instabilities similar to those in the expanding case.

Contribution

It extends previous work by numerically analyzing the contracting direction, revealing that instabilities occur for all $0 \\leq K < 1/3$, and characterizing the behavior of density gradients near the big bang.

Findings

Instabilities are present in the contracting direction for $0 \\leq K < 1/3$.

Density gradients develop steep, unbounded profiles near the big bang.

Similar behavior to the expanding case near timelike infinity.

Abstract

Using numerical methods, we examine, under a Gowdy symmetry assumption, the dynamics of nonlinearly perturbed FLRW fluid solutions of the Einstein-Euler-scalar field equations in the contracting direction for linear equations of state $p = K\rho$ and sound speeds $0\leq K<1/3$. This article builds upon the numerical work from \cite{BMO:2023} in which perturbations of FLRW solutions to the Einstein-Euler equations with positive cosmological constant in the expanding time direction were studied. The numerical results presented here confirm that the instabilities observed in \cite{BMO:2023,MarshallOliynyk:2022} for $1/3<K<1$, first conjectured to occur in the expanding direction by Rendall in \cite{Rendall:2004}, are also present in the contracting direction over the complementary parameter range $0\leq K<1/3$. Our numerical solutions show that the fractional density gradient of the nonlinear perturbations develop steep gradients near a finite number of spatial points and become unbounded towards the big bang. This behaviour, and in particular the characteristic profile of the fractional density gradient near the big bang, is strikingly similar to what was observed in the expanding direction near timelike infinity in the article \cite{BMO:2023}.