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

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}.