宇宙学初始数据集的Ricci流形变
Ricci flow deformation of cosmological initial data sets
摘要：
在广义相对论中，宇宙学初始数据集的里奇流变形是一种生成初始数据集族的技术，它可能允许在不同的时空之间进行插值。自从里奇流出现以来，这个想法就一直存在，但很难将其转化为合理的数学过程。在这个简短的谈话中，我们说明，如何佩雷尔曼最近的结果在里奇流理论可以大大改善这种情况。从物理学的角度来看，这种分析可以与为非均匀宇宙找到一个常数曲率模板时空的问题有关，与观测数据的解释有关，因此与暗能量和暗物质的争论有关。这些技术提供了控制曲率波动（内在的反反应项）在其关系的平均物质分布。
英文摘要：
Ricci flow deformation of cosmological initial data sets in general relativity is a technique for generating families of initial data sets which potentially would allow to interpolate between distinct spacetimes. This idea has been around since the appearance of the Ricci flow on the scene, but it has been difficult to turn it into a sound mathematical procedure. In this expository talk we illustrate, how Perelman's recent results in Ricci flow theory can considerably improve on such a situation. From a physical point of view this analysis can be related to the issue of finding a constant-curvature template spacetime for the inhomogeneous Universe, relevant to the interpretation of observational data and, hence, bears relevance to the dark energy and dark matter debates. These techniques provide control on curvature fluctuations (intrinsic backreaction terms) in their relation to the averaged matter distribution.
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