MG12 - Talk detail
 

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Abstract

The Generic Cosmological Flow: A Review of Recent Results and Open Problems

We discuss recent progress in the problem of the asymptotic state and formation of singularities of a cosmological spacetime that is generic in the sense of possessing no exceptional properties of any kind. In this respect, we review the Hamiltonian reduction methods of Fischer and Moncrief, the volume monotonicity results of M. T. Anderson based on the Cheeger-Gromov theory of Riemannian convergence, and the global existence of S^1-invariant universes and hyperbolic cones by Choquet-Bruhat, Isenberg, Moncrief and others. For the singularity behaviour of generic cosmologies, we analyze the approaches to the BKL conjecture and the global attractor through representation theory developed by Damour, Nicolai and others, and the related VTD and non-VTD results. We also discuss new results on gluing and non-CMC evolution and their possible relevance to cosmology, and describe how the idea of surgery in the Ricci flow helped to reach geometrization in ways that could be relevant for the cosmological flow.

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