Decay of solutions of the wave equation in expanding cosmological spacetimes

TL;DR

This paper investigates how solutions to the wave equation diminish over time in certain expanding universe models, providing improved decay estimates especially in accelerated expansion scenarios.

Contribution

It introduces a new partial energy method and iteration scheme to derive sharper decay rates for wave solutions in expanding cosmological spacetimes.

Findings

Faster decay rates for wave solutions with finite higher order energies.

Decay rates are nearly optimal in accelerated expansion models.

Enhanced understanding of wave behavior in cosmological backgrounds.

Abstract

We study the decay of solutions of the wave equation in some expanding cosmological spacetimes, namely flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) models and the cosmological region of the Reissner-Nordstr\"om-de Sitter (RNdS) solution. By introducing a partial energy and using an iteration scheme, we find that, for initial data with finite higher order energies, the decay rate of the time derivative is faster than previously existing estimates. For models undergoing accelerated expansion, our decay rate appears to be (almost) sharp.