We have investigated the cosmological scenarios with a four dimensional
effective action which is connected with multidimensional, supergravity and
string theories. The solution for the scale factor is such that initially
universe undergoes a decelerated expansion but in late times it enters into the
accelerated expansion phase. Infact, it asymptotically becomes a de-Sitter
universe. The dilaton field in our model is a decreasing function of time and
it becomes a constant in late time resulting the exit from the scalar tensor
theory to the standard Einstein's gravity. Also the dilaton field results the
existence of a positive cosmological constant in late times.Comment: 7 pages, Revtex Style, 6 Postscript figure