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–Lemaître–Robertson–Walker 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.