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.
ACKNOWLEDGMENTS
This work was supported by Project Nos. PTDC/MAT/108921/2008 and CERN/FP/116377/2010, and by CMAT, Universidade do Minho, and CAMSDG, Instituto Superior Técnico, through FCT plurianual funding. A.A. thanks the Mathematics Department of Instituto Superior Técnico (Lisbon), where this work was done, for hospitality, and FCT for Grant No. SFRH/BD/48658/2008.
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