Decay of solutions to the Klein-Gordon equation on some expanding cosmological spacetimes
Abstract: 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.
AT THIS PAGE YOU CAN DOWNLOAD THE WHOLE ESSAY. (follow the link to the next page)