On multidimensional cosmological solutions with scalar fields and 2-forms corresponding to rank-3 lie algebras: Acceleration and small variation of G

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(τ) (τ is the cosmological time). This interval contains τ 0 at which G(gt) has a minimum. Special solutions with three phantom scalar fields are analyzed. It is shown that in the vicinity of τ 0 the time variation of G(τ) 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 τ → ∞. Exact solutions with asymptotically exponential accelerated expansion of 3D space are also considered.