  We consider solutions of the cosmological equations pertaining to a
dissipative, dilaton-driven off-equilibrium Liouville Cosmological model, which
may describe the effective field theoretic limit of a non-critical string model
of the Universe. The non-criticality may be the result of an early-era
catastrophic cosmic event, such as a big-bang, brane-world collision etc. The
evolution of the various cosmological parameters of the model are obtained, and
the effects of the dilaton and off-shell Liouville terms, including briefly
those on relic densities, which distinguish the model from conventional
cosmologies, are emphasised.
