On multidimensional cosmological solutions with scalar fields and 2-forms corresponding to rank-3 lie algebras: Acceleration and small variation of G
A.A. Golubtsova^{1}
(1) Institute of Gravitation and Cosmology, Peoples' Friendship University of Russia, ul. Miklukho-Maklaya 6, Moscow 117198, Russia
Abstract
In a simple multidimensional model we study the possibility of accelerated expansion of a 3-dimensional subspace combined with variation of the effective 4-dimensional constant of gravity within experimental constraints. Multidimensional cosmological solutions with m 2-form fields and l scalar fields are presented. Solutions corresponding to rank-3 Lie algebras are singled out and discussed. Each of the solutions contains two factor spaces: the one-dimensional space M_{1} and the Ricci-flat space M_{2}. A 3-dimensional subspace of M_{2} is interpreted as our space. We show that, if at least one of the scalar fields is of phantom nature, there exists a time interval where accelerated expansion of our 3D space is compatible with a small enough variation of the effective gravitational constant G(t) (t is the cosmological time). This interval contains t_{0} at which G(t) has a minimum. Special solutions with three phantom scalar fields are analyzed. It is shown that in the vicinity of t_{0} the time variation of G(t) decreases in the sequence of Lie algebras A_{3}, C_{3} and B_{3} in the family of solutions with asymptotic power-law behavior of the scale-factors as t® ¥. Exact solutions with asymptotically exponential accelerated expansion of 3D space are also considered.
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