Billiard Representation for Multidimensional Cosmology with P-Branes Near the Singularity (original) (raw)

The Chaotic Universe, 2000

Abstract

Cosmological model describing the evolution of n Einstein spaces in the theory with l scalar fields and forms is considered. When electro-magnetic composite pbrane ansatz is adopted, and certain restrictions on the parameters of the model are imposed, the dynamics of the model near the singularity is reduced to a billiard on the (N -1)-dimensional Lobachevsky space HN-1, N = n +l. The geometrical criterion for the finiteness of the billiard volume and its compactness is used. This criterion reduces the problem to the problem of illumination of a sphere SN-2 by point-like sources. Some examples with billiards of finite volume and hence oscillating behaviour near the singularity are considered. Among them examples with square and triangle 2-dimensional billiards (e.g. that of the Bianchi-IX model) and a 4-dimensional billiard in "truncated" D = 11 supergravity model are considered.

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