Inhomogeneous perturbations of plane-wave spacetimes

TL;DR

This paper investigates the stability of vacuum plane-wave solutions in cosmology, demonstrating that they are unstable to generic inhomogeneous perturbations due to divergence in key variables.

Contribution

It provides the first analysis of inhomogeneous perturbations of plane-wave spacetimes, revealing their instability in a cosmological context.

Findings

Plane-wave solutions are unstable to generic inhomogeneous perturbations.

Divergence of expansion-normalised frame variables causes instability.

Results suggest limitations of these solutions as late-time attractors.

Abstract

Recently it was shown that the exact cosmological solutions known as the vacuum plane-wave solutions are late-time attractors for an open set of the spatially homogeneous Bianchi universes containing a non-inflationary $\gamma$-law perfect fluid. In this paper we study inhomogeneous perturbations of these plane-wave spacetimes. By using expansion-normalised scale-invariant variables we show that these solutions are unstable to generic inhomogeneous perturbations. The crucial observation for establishing this result is a divergence of the expansion-normalised frame variables which ultimately leads to unstable modes.