Decay of solutions of the wave equation in expanding cosmological spacetimes

Abstract

We study the decay of solutions of the wave equation in some expanding cosmological spacetimes, namely flat Friedmann-Lemaître-Robertson-Walker (FLRW) models and the cosmological region of the Reissner-Nordström-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.

25 pages, 3 figures; v2: small corrections; v3: typos corrected, matches final published version; v4: typo in the statement of Theorem 2 corrected; v5: sign error in the conformally invariant wave equation fixed