Decay of solutions of the wave equation in cosmological spacetimes -- a numerical analysis

TL;DR

This paper numerically investigates how solutions to the linear wave equation decay over time in expanding cosmological spacetimes, revealing a relationship between universe expansion and wave decay rates, with tails playing a key role.

Contribution

It provides a numerical analysis of wave decay in FLRW spacetimes, including hyperbolic cases, and identifies the influence of tails on decay mechanisms.

Findings

Decay rates depend on the universe's expansion rate.

Tails significantly influence the decay process.

Quantitative relations between background expansion and wave decay are established.

Abstract

We numerically evolve spherically symmetric solutions to the linear wave equation on some expanding Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetimes and study the respective asymptotics for large times. We find a quantitative relation between the expansion rate of the underlying background universe and the decay rate of linear waves, also in the context of spatially-hyperbolic spacetimes, for which rigorous proofs of decay rates are not generally known. A prominent role in the decay mechanism is shown to be played by tails, i.e. scattered waves propagating in the interior of the lightcone.