Spherical linear waves in de Sitter spacetime

Abstract

We apply Christodoulou's framework, developed to study the Einstein-scalar eld equations in spherical symmetry, to the linear wave equation in de Sitter spacetime, as a rst step towards the Einstein-scalar eld equations with positive cosmological constant. We obtain an integro-di erential 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.