Instability of Slowly Expanding FLRW Spacetimes

TL;DR

This paper numerically investigates the nonlinear stability of decelerating FLRW spacetimes under perturbations, revealing that shocks form in finite time for all tested equations of state, contrasting with accelerated cases.

Contribution

It provides the first numerical evidence that perturbations in decelerating FLRW spacetimes develop shocks, highlighting a fundamental instability not present in accelerated models.

Findings

Perturbations lead to shock formation in finite time for all K values.

Contrasts with accelerated FLRW spacetimes where shocks are suppressed.

Numerical simulations confirm the instability of decelerating FLRW solutions.

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 $0\leq K\leq 1$. 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.