Billiard representation for multidimensional multi-scalar cosmological model with exponential potentials

Details Billiard representation for multidimensional multi-scalar cosmological model with exponential potentials Billiard representation for multidimensional multi-scalar cosmological model with exponential potentials

2003-12-30

arxiv.org/abs/hep-th/0312317v1

Gen.Rel.Grav. 36 (2004) 1563-1578

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, Latex, 2 figures; to be published in GRG

Scientific paper

10.1023/B:GERG.0000032149.58989.

Multidimensional cosmological-type model with n Einstein factor spaces in the theory with l scalar fields and multiple exponential potential is considered. The dynamics of the model near the singularity is reduced to a billiard on the (N-1)-dimensional Lobachevsky space H^{N-1}, N = n+l. It is shown that for n > 1 the oscillating behaviour near the singularity is absent and solutions have an asymptotical Kasner-like behavior. For the case of one scale factor (n =1) billiards with finite volumes (e.g. coinciding with that of the Bianchi-IX model) are described and oscillating behaviour of scalar fields near the singularity is obtained.

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