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

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 M1 and the Ricci-flat space M2. A 3-dimensional subspace of M2 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 τ0 at which G(gt) has a minimum. Special solutions with three phantom scalar fields are analyzed. It is shown that in the vicinity of τ0 the time variation of G(τ) decreases in the sequence of Lie algebras A3, C3 and B3 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. © 2010 Pleiades Publishing, Ltd.