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Billiard Representation for Multidimensional Multi-Scalar Cosmological Model with Exponential Potentials

2004; Springer Science+Business Media; Volume: 36; Issue: 7 Linguagem: Inglês

10.1023/b

1572-9532

H. Dehnen, В. Д. Иващук, V. N. Melnikov,

Advanced Mathematical Theories and Applications

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.