Fundamental solutions for the Klein-Gordon equation in de Sitter spacetime

Abstract

In this article we construct the fundamental solutions for the Klein-Gordon equation in de Sitter spacetime. We use these fundamental solutions to represent solutions of the Cauchy problem and to prove L p − L q estimates for the solutions of the equation with and without a source term. 0 Introduction and Statement of Results In this paper we construct the fundamental solutions for the Klein-Gordon equation in the de Sitter spacetime and use these fundamental solutions to find representations of the solutions to the Cauchy problem as well as L p − L q estimates for them. After averaging on a suitable scale, our universe is homogeneous and isotropic; therefore, the properties