  Liouville string theory is a natural framework for discussing the
non-equilibrium evolution of the Universe. It enables non-critical strings to
be treated in mathematically consistent manner, in which target time is
identified with a world-sheet renormalization-group scale parameter, preserving
target-space general coordinate invariance and the existence of an S-matrix. We
review our proposals for a unified treatment of inflation and the current
acceleration of the Universe. We link the current acceleration of the Universe
with the value of the string coupling. In such a scenario, the dilaton plays an
essential background role, driving the acceleration of the Universe during the
present era after decoupling as a constant during inflation.
