  We perform fits of unconventional dark energy models to the available data
from high-redshift supernovae, distant galaxies and baryon oscillations. The
models are based either on brane cosmologies or on Liouville strings in which a
relaxation dark energy is provided by a rolling dilaton field (Q-cosmology). An
interesting feature of such cosmologies is the possibility of effective
four-dimensional negative-energy dust and/or exotic scaling of dark matter. An
important constraint that can discriminate among models is the evolution of the
Hubble parameter as a function of the redshift, H(z). We perform fits using a
unifying formula for the evolution of H(z), applicable to different models. We
find evidence for a negative-energy dust at the current era, as well as for
exotic-scaling (a^{-delta}) contributions to the energy density, with
3.3<delta<4.3. The latter could be due to dark matter coupling with the dilaton
in Q-cosmology models, but it is also compatible with the possibility of dark
radiation from a brane Universe to the bulk in brane-world scenarios, which
could also encompass Q-cosmology models. The best-fit model seems to include an
a^{-2}-scaling contribution to the energy density of the Universe, which is
characteristic of the dilaton relaxation in Q-cosmology models, not to be
confused with the spatial curvature contribution of conventional cosmology. We
conclude that Q-cosmology fits the data equally well with the Lambda-CDM model
for a range of parameters that are in general expected from theoretical
considerations.
