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. © 2010 Elsevier Inc. All rights reserved