On `graceful exitʹ from inflationary phase in two-dimensional Liouville string cosmology

Within the context of a super-critical (Liouville) string, we discuss (target-space) two-dimensional string cosmology. A numerical analysis indicates that the identification of time with the Liouville mode results in an expanding universe with matter which exhibits an inflationary phase, and `graceful exitʹ from it, tending asymptotically to a flat-metric fixed point. This fixed point is characterized by a dilaton configuration which, depending on the initial conditions, either decreases linearly with the cosmic time, or is a finite constant. The rôle of matter in inducing such phenomena is emphasized. Although preliminary, this toy model seems to share all the features expected to characterize a phenomenologically acceptable cosmological string model.