Decay of solutions to the Klein-Gordon equation on some expanding cosmological spacetimes

Sammanfattning: The decay of solutions to the Klein-Gordon equation is studied in two expanding cosmological spacetimes, namely (1) the de Sitter universe in flat Friedmann-Lemaitre-Robertson-Walker (FLRW) form, and (2) the cosmological region of the Reissner-Nordström-de Sitter (RNdS) model. Using energy methods, for initial data with finite higher order energies, bounds on the decay rates of the solution are obtained. Also, a previously established bound on the decay rate of the time derivative of the solution to the wave equation, in an expanding de~Sitter universe in flat FLRW form, is improved, proving Rendall's conjecture. A similar improvement is also given for the wave equation in the cosmological region of the RNdS spacetime.