Cosmological Billiards

By T. Damour, M. Henneaux, H. Nicolai. 2002

293 citations recorded by the source corpus.

It is shown in detail that the dynamics of the Einstein-dilaton-pform system in the vicinity of a spacelike singularity can be asymptotically described, at a generic spatial point, as a billiard motion in a region of Lobachevskii space (realized as an hyperboloid in the space of logarithmic scale factors). This is done within the Hamiltonian formalism, and for an arbitrary number of spacetime dimensions D ≥ 4. A key rôle in the derivation is played by the Iwasawa decomposition of the spatial metric, and by the fact that the off-diagonal degrees of freedom, as well as the p-form degrees of freedom, get “asymptotically frozen” in this description. For those models admitting a Kac-Moody theoretic interpretation of the billiard dynamics we outline how to set up an asymptotically equivalent description in terms of a one-dimensional non-linear σ-model formally invariant under the corresponding Kac-Moody group.

Subfields: Astronomy and Astrophysics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/28f5ff1587e21d61153e5901c60e52e8c422d953

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Citations in the corpus

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The gauge structure of generalised diffeomorphisms (2012, background): “The series can even be continued to the infinite-dimensional algebras E9 [4, 5], E10 [6–10] and E11 [11–15], although the interpretation is somewhat different in the last two cases.”
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