Any $2+1$ dimensional Einsteinian spacetime with positive cosmological constant and compact hyperbolic spatial topology evolves in the expanding direction to a de Sitter model with homogeneous hyperbolic spatial geometry. In particular, the latter constitutes the uniform future attractor for this class of spacetimes for arbitrary large initial data. This is an example of large-data homogenization and demonstrates the ability of gravitation to cause late time homogenization in the evolution of cosmological models independently of their initial state.

中文翻译：

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2 + 1维Λ重力中的未来吸引子

任何 $2+\mathrm{1个}$具有正宇宙学常数和紧凑双曲空间拓扑的维爱因斯坦时空在扩展方向上演化为具有均匀双曲空间几何形状的de Sitter模型。特别地，对于任意大的初始数据，后者构成此类时空的统一未来吸引子。这是大数据均质化的一个示例，并证明了引力能够在宇宙学模型的演化中引起后期均质化，而与初始状态无关。