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

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.