We prove nonlinear stability for a large class of solutions to the Einstein equations with a positive cosmological constant and compact spatial topology in arbitrary dimensions, where the spatial metric is Einstein with either positive or negative Einstein constant. The proof uses the CMC Einstein flow and stability follows by an energy argument. We prove in addition that the development of non-CMC initial data close to the background contains a CMC hypersurface, which in turn implies that stability holds for arbitrary perturbations. Furthermore, we construct a one-parameter family of initial data such that above a critical parameter value the corresponding development is future and past incomplete.

中文翻译：

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具有正宇宙常数的爱因斯坦流的稳定不动点

我们证明了爱因斯坦方程的一大类解的非线性稳定性，它具有正宇宙常数和任意维度的紧凑空间拓扑，其中空间度量是爱因斯坦，爱因斯坦常数为正或负。证明使用 CMC 爱因斯坦流和稳定性遵循能量论证。此外，我们证明靠近背景的非 CMC 初始数据的发展包含 CMC 超曲面，这反过来意味着稳定性适用于任意扰动。此外，我们构建了一个初始数据的单参数族，使得高于关键参数值的相应发展是未来和过去不完整的。