Spherical linear waves 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.

9 pages, 1 figure; v2: minor changes, references added, matches final published version

References in corpus (2)

• Fundamental Solutions for the Klein-Gordon Equation in de Sitter Spacetime
• The wave equation on Schwarzschild-de Sitter spacetimes

Cited by in corpus (6)

• Global existence of the self-interacting scalar field in the de Sitter universe
• Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI${}_0$
• Future dynamics of FLRW for the massless-scalar field system with positive cosmological constant
• Decay of solutions of the wave equation in expanding cosmological spacetimes
• The spherically symmetric Einstein-scalar field system with positive and vanishing cosmological constant: a comparison
• Integral transform approach to solving Klein-Gordon equation with variable coefficients