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.

arXiv comment25 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

References in corpus (6)

• Asymptotics of solutions of the Einstein equations with positive cosmological constant
• Asymptotics of linear waves and resonances with applications to black holes
• Global results for linear waves on expanding Kerr and Schwarzschild de Sitter cosmologies
• A Note on Wave Equation in Einstein & de Sitter Spacetime
• On the initial value problem for the wave equation in Friedmann -- Robertson -- Walker space-times
• Spherical linear waves in de Sitter spacetime

Cited by in corpus (5)

• Future dynamics of FLRW for the massless-scalar field system with positive cosmological constant
• Explicit formulas and decay rates for the solution of the wave equation in cosmological spacetimes
• Decay of solutions of the wave equation in cosmological spacetimes -- a numerical analysis
• Semilinear wave equations on accelerated expanding FLRW spacetimes
• Hyperboloidal approach for linear and non-linear wave equations in FLRW spacetimes