Ricci flow deformation of cosmological initial data sets

Details Ricci flow deformation of cosmological initial data sets Ricci flow deformation of cosmological initial data sets

2008-01-03

arxiv.org/abs/0801.0553v1

N.Manganaro, R.Monaco, S.Rionero (eds) World Scientific (2008) 118-127

Physics

Mathematical Physics

Invited Talk presented at WASCOM 07, 14th International Conference on Waves and Stability in Continuous Media, Scicli (Ragusa,

Scientific paper

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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