Asymptotically de Sitter metrics from scattering data in all dimensions

Abstract

In spacetime dimensions $n+1\ge 4$, we show the existence of solutions of the Einstein vacuum equations which describe asymptotically de Sitter spacetimes with prescribed smooth data at the conformal boundary. This provides a short alternative proof of a special case of a result by Shlapentokh-Rothman and Rodnianski, and generalizes earlier results by Friedrich and Anderson to all dimensions.

arXiv comment14 pages, 1 figure. To appear in Phil. Trans. A; related to a talk at the Royal Society meeting "At the interface of asymptotics, conformal methods and analysis in general relativity", London, May 9-10, 2023