Fundamental Solutions for Wave Equation in de Sitter Model of Universe

TL;DR

This paper constructs fundamental solutions for the wave equation in the de Sitter universe model, enabling analysis of solution behavior and decay estimates in this cosmological setting.

Contribution

It introduces explicit fundamental solutions for the wave equation in the de Sitter universe, facilitating solution representation and decay analysis.

Findings

Derived explicit fundamental solutions for the wave equation in de Sitter space

Established $L^p-L^q$ decay estimates for solutions

Provided methods for solving the Cauchy problem in this context

Abstract

In this article we construct the fundamental solutions for the wave equation arising in the de Sitter model of the universe. We use the fundamental solutions to represent solutions of the Cauchy problem and to prove the $L^p-L^q$-decay estimates for the solutions of the equation with and without a source term.