  Non-critical string cosmologies may be viewed as the analogue of
off-equilibrium models arising within string theory as a result of a cosmically
catastrophic event in the early Universe. Such models entail relaxing-to-zero
dark energies provided by a rolling dilaton field at late times. We discuss
fits of such non-critical models to high-redshift supernovae data, including
the recent ones by HST and ESSENCE and compare the results with those of a
conventional model with Cold Dark Matter and a cosmological constant and a
model invoking super-horizon perturbations.
