Liouville cosmology at zero and finite temperatures

We discuss cosmology in the context of Liouville strings, characterized by a centralcharge deficit Q(2), in which target time is identified with (the worldsheet zero mode of the) Liouville field: Q-Cosmology. We use a specific example of colliding braneworlds to illustrate the phase diagram of this cosmological framework. The collision provides the necessary initial cosmological instability, expressed as a departure from conformal invariance in the underlying string model. The brane motion provides a way of breaking target-space supersymmetry, and leads to various phases of the brane and bulk Universes. Specifically, we find a hot metastable phase for the bulk string Universe soon after the brane collision in which supersymmetry is broken, which we describe by means of a subcritical worldsheet sigma-model dressed by a spacelike Liouville field, representing finite temperature (Euclidean time). This phase is followed by an inflationary phase for the brane Universe, in which the bulk string excitations are cold. This is described by a super-critical Liouville string with a timelike Liouville mode, whose zero mode is identified with the Minkowski target time. Finally, we speculate on possible ways of exiting the inflationary phase, either by means of subsequent collisions or by deceleration of the brane Universe due to closed-string radiation from the brane to the bulk. While phase transitions from hot to cold configurations occur in the bulk string universe, stringy excitations attached to the braneworld remain thermalized. throughout, at a temperature which can be relatively high. The late-time behavior of the model results in dilaton-dominated dark energy and present-day acceleration of the expansion of the Universe, asymptoting eventually to zero.