On non-singular solutions in multidimensional cosmology

Exact solutions with an exponential behaviour of the scale factors are considered in a multidimensional cosmological model describing the dynamics of n + 1 Ricci-flat factor spaces Mi in the presence of a one-component perfect fluid. The pressures in all spaces are proportional to the density: pi = wiρ, i = 0,⋯,n. Solutions with accelerated expansion of our 3-space M0 and a small enough variation of the gravitational constant G are found. A family of generalized non-singular S-brane solutions with orthogonal intersection rules and n Ricci-flat factor spaces in the theory with several scalar fields, antisymmetric forms and multiple scalar potential is considered. The solution possess exponential behaviour of scale factors. These solutions contain a sub-family of solutions with accelerated expansion of certain factor spaces. Some examples of solutions with exponential dependence of one scale factor and constant scale factors of "internal" spaces (e.g. Freund-Rubin type solutions) are also considered. © 2009 American Institute of Physics.