In space–time dimensions n + 1 ≥ 4 , we show the existence of solutions of the Einstein vacuum equations which describe asymptotically de Sitter space–times 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 of Friedrich and Anderson to all dimensions. This article is part of a discussion meeting issue ‘At the interface of asymptotics, conformal methods and analysis in general relativity’.

中文翻译：

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来自所有维度的散射数据的渐近德西特度量

在时空维度上 n + 1 ≥ 4 ，我们证明了爱因斯坦真空方程解的存在性，该方程用共形边界处的规定光滑数据渐近地描述德西特时空。这为 Shlapentokh-Rothman 和 Rodnianski 的结果的特殊情况提供了简短的替代证明，并将 Friedrich 和 Anderson 的早期结果推广到所有维度。本文是讨论会议问题“渐进、共形方法和广义相对论分析的接口”的一部分。