Spherical linear waves in de Sitter spacetime

TL;DR

This paper studies linear wave behavior in de Sitter spacetime using Christodoulou's framework, deriving decay properties and boundedness results, as a step towards understanding Einstein-scalar field equations with positive cosmological constant.

Contribution

It applies Christodoulou's framework to linear waves in de Sitter spacetime, providing elementary derivations of decay and boundedness properties as a foundation for future nonlinear studies.

Findings

Linear waves are bounded by initial data.

Exponential decay of waves in Bondi time.

Established Price law in de Sitter spacetime.

Abstract

We apply Christodoulou's framework, developed to study the Einstein-scalar field equations in spherical symmetry, to the linear wave equation in de Sitter spacetime, as a first step towards the Einstein-scalar field equations with positive cosmological constant. We obtain an integro-differential evolution equation which we solve by taking initial data on a null cone. As a corollary we obtain elementary derivations of expected properties of linear waves in de Sitter spacetime: boundedness in terms of (characteristic) initial data, and a Price law establishing uniform exponential decay, in Bondi time, to a constant.