Instability of Slowly Expanding FLRW Spacetimes

Abstract

We numerically study, under a Gowdy symmetry assumption, nonlinear perturbations of the decelerated FLRW fluid solutions to the Einstein-Euler system toward the future for linear equations of state $p=K\rho$ with $0\le K\le 1$. This article builds on the work of Fajman et al. (2024 arXiv:2405.03431) in which perturbations of the homogeneous fluid solution on a fixed, decelerating FLRW background were studied. Our numerical results show that for all values of $K$, perturbations of the FLRW solution develop shocks in finite time. This behaviour contrasts known results for spacetimes with accelerated expansion in which shock formation is suppressed.

arXiv commentMaterial added to address referee comments. Agrees with published version. 22 pages, 13 figures