The graceful exit problem in string cosmology

Isotropic string cosmology can be classified into duality related branches:one can be connected smoothyto an expanding Friedman-Robertson-Walker Universe, the describes accelerated inflation or contraction. We showthat, if the dilation potential has certain generic properties, the two branches can evolve smoothy into each other. We find,however, that just the effects of a potential do not allow for a graceful exit from accelerated inflation in the weak curvatureregime. We explain how conformal field theory techniques could be used to give a decisive answer on whether graceful exitfrom accelerated inflation is possible at all.