On 'graceful exit' from inflationary phase in two-dimensional Liouville string cosmology

Within the context of a super-critical (Liouville) string, we discuss (targ et-space) two-dimensional string cosmology. A numerical analysis indicates that the identification of time with the Liouville mode results in an expan ding universe with matter which exhibits an inflationary phase, and 'gracef ul exit' from it, tending asymptotically to a flat-metric fixed point. This fixed point is characterized by a dilaton configuration which, depending o n the initial conditions, either decreases linearly with the cosmic time, o r is a finite constant. The role of matter in inducing such phenomena is em phasized. Although preliminary, this toy model seems to share all the featu res expected to characterize a phenomenologically acceptable cosmological s tring model. (C) 1999 Published by Elsevier Science B.V. All rights reserve d.