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.
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Research Article| May 25 2012
Spherical linear waves in de Sitter spacetime
João L. Costa;
João L. Costa, Artur Alho, José Natário; Spherical linear waves in de Sitter spacetime. J. Math. Phys. 1 May 2012; 53 (5): 052501. https://doi.org/10.1063/1.4721644
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