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

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.