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By means of a simple model we investigate the possibility of an acceleratedexpansion of a 3-dimensional subspace in the presence of the variation of theeffective 4-dimensional constant obeying the experimental constraint.Multidimensional cosmological solutions with m 2-form fields and l scalarfields are presented. Solutions corresponding to rank-3 Lie algebras aresingled out and discussed. Each of solutions contain two factor spaces:one-dimensional space M_1 and Ricci-flat space M_2. A 3-dimensional subspace ofM_2 is interpreted as "our" space. We show that there exists a time intervalwhere accelerated expansion of our 3D space is compatible with a small enoughvariation of the effective gravitational constant G(\tau). This intervalcontains \tau_0 which is the point of minimum of G(\tau) (here \tau is thesynchronous time variable). Special solutions with three phantom scalar fieldsare analyzed. It is shown that in the vicinity of the point \tau_0 the timevariation of G(\tau) decreases in the sequence of Lie algebras A_3, C_3 and B_3when the solutions with asymptotically power-law behavior of scale-factors for\tau \to \infty are considered. Exact solutions with asymptotically exponentialaccelerated expansion of 3D space are also considered.

gravitation and cosmology/gravitation and cosmology

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