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 de Sitter universe flat Friedmann–Lemaître–Robertson–Walker (FLRW) form and region Reissner–Nordström–de (RNdS) model. Using energy methods, for initial data with finite higher-order energies, rates solution are obtained. Also, a previously established rate time derivative wave equation, an FLRW form, improved, proving Rendall’s conjecture. A similar improvement also given RNdS spacetime.