ar X iv : h ep - t h / 07 01 02 9 v 3 1 F eb 2 00 7 T and S dualities and The cosmological evolution of the dilaton and the scale factors

Cosmologically stabilizing radion along with the dilaton is one of the major concerns of low energy string theory. One can hope that T and S dualities can provide a plausible answer. In this work we study the impact of S and T duality invariances on dilaton gravity. We have shown various instances where physically interesting models arise as a result of imposing the mentioned invariances. In particular S duality has a very privileged effect in that the dilaton equations partially decouple from the evolution of the scale factors. This makes it easy to understand the general rules for stabilization of the dilaton. We also show that certain T duality invariant actions become S duality invariance compatible, that is they mimic S duality when extra dimensions stabilize. Implying both T and S duality invariances when all spatial dimensions were compact we find a possible bounce solution for the scale factors in a Hagedorn-like gas.