Phase transition between shock formation and stability in cosmological fluids

TL;DR

This paper identifies a phase transition in cosmological fluids where stability shifts to instability when the fluid's sound speed surpasses a critical threshold related to the universe's expansion rate, supported by analytical and numerical evidence.

Contribution

It introduces a precise relationship between the expansion parameter and sound speed that delineates stable and unstable fluid behaviors in cosmological models.

Findings

Established a critical line separating stable and unstable regimes.

Proved stability in the first region using rigorous techniques.

Numerical experiments confirmed the sharpness of the stability boundary.

Abstract

We demonstrate a novel phase transition from stable to unstable fluid behaviour for fluid-filled cosmological spacetimes undergoing decelerated expansion. This transition occurs when the fluid speed of sound $c_S$ exceeds a critical value relative to the expansion rate $a(t) = t^\alpha$ of spacetime. We present an explicit relationship between $\alpha$ and $c_S$ , which subdivides the $(\alpha,c_S)$-parameter space into two regions. Using rigorous techniques, we establish stability of quiet fluid solutions in the first stable region. Numerical experiments reveal that the complement of the stable region consists of unstable solutions, implying sharpness of our stability result. We provide a definitive analytical bound and high-precision numerical evidence for the exact location of the critical line separating the stable from the unstable region.