A parametrix for the fundamental solution of the Klein–Gordon equation on asymptotically de Sitter spaces

In this paper we construct a parametrix for the forward fundamental solution of the wave and Klein–Gordon equations on asymptotically de Sitter spaces without caustics. We use this parametrix to obtain asymptotic expansions for solutions of (□−λ)u=f and to obtain a uniform Lp estimate for a family of bump functions traveling to infinity.