A Strichartz estimate for de Sitter space

TL;DR

This paper establishes Strichartz estimates for the Klein-Gordon equation on asymptotically de Sitter spaces, extending known results to a broader class of metrics and applying them to semilinear equations.

Contribution

It introduces a family of Strichartz estimates for conformally invariant Klein-Gordon equations on asymptotically de Sitter spaces with C^2 metrics, including de Sitter space itself.

Findings

Established Strichartz estimates for a class of asymptotically de Sitter spaces.

Applied the estimates to analyze semilinear Klein-Gordon equations.

Extended known estimates to less regular, C^2 metric settings.

Abstract

We demonstrate a family of Strichartz estimates for the conformally invariant Klein-Gordon equation on a class of asymptotically de Sitter spaces with C^2 metrics by using well-known local Strichartz estimates and a rescaling argument. This class of metrics includes de Sitter space. We also give an application of the estimates to a semilinear Klein-Gordon equation on these spaces.