Future instability of FLRW fluid solutions for linear equations of state $p=K\rho$ with $1/3 <K<1$

TL;DR

This paper uses numerical simulations to demonstrate that FLRW fluid solutions with linear equations of state ($p=K ho$, for $1/3<K<1$) exhibit future instabilities characterized by unbounded density contrasts, challenging standard cosmological models.

Contribution

It extends previous fixed-background studies by numerically analyzing the coupled Einstein-Euler system, confirming the presence of instabilities in a full gravitational setting for the entire parameter range.

Findings

Density contrast develops steep gradients and becomes unbounded at future infinity.

Instabilities are present when coupling gravity, not just in fixed backgrounds.

Results challenge the standard cosmological expansion paradigm.

Abstract

Using numerical methods, we examine the dynamics of nonlinear perturbations in the expanding time direction, under a Gowdy symmetry assumption, of FLRW fluid solutions to the Einstein-Euler equations with a positive cosmological constant $\Lambda>0$ and a linear equation of state $p = K\rho$ for the parameter values $1/3<K<1$. This paper builds upon the numerical work in \cite{Marshalloliynyk:2022} in which the simpler case of a fluid on a fixed FLRW background spacetime was studied. The numerical results presented here confirm that the instabilities observed in \cite{Marshalloliynyk:2022} are also present when coupling to gravity is included as was previously conjectured in \cite{Rendall:2004,Speck:2013}. In particular, for the full parameter range $1/3 < K <1$, we find that the density contrast of the nonlinear perturbations develop steep gradients near a finite number of spatial points and becomes unbounded there at future timelike infinity. This instability is of particular interest since it is not consistent with the standard picture for late time expansion in cosmology.