Cosmology in scalar-tensor theory and asymptotically de Sitter universe

We have investigated the cosmological scenarios with a four-dimensional eff ective action which is connected with multidimensional, supergravity and st ring theories. The solution for the scale factor is such that initially uni verse undergoes a decelerated expansion but in late times it enters into th e accelerated expansion phase. In fact, it asymptotically becomes a de Sitt er universe. The dilaton field in our model is a decreasing function of tim e 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 r esults in the existence of a positive cosmological constant in late times.