Decay of solutions to the Klein-Gordon equation on some expanding cosmological spacetimes
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 obOne of the most profound realisations of physics of the twentieth century is that space and time should be considered as a single whole, a four-dimensional geometric object called spacetime, rather than two separate entities. Gravitation arising from matter manifests itself as curvature of spacetime, and the motion of matter is described by the straightest possible curves on this curved spacetime.