  In this article we investigate the properties of the FLRW flat cosmological
models in which the cosmic expansion of the Universe is affected by a dilaton
dark energy (Liouville scenario). In particular, we perform a detailed study of
these models in the light of the latest cosmological data, which serves to
illustrate the phenomenological viability of the new dark energy paradigm as a
serious alternative to the traditional scalar field approaches. By performing a
joint likelihood analysis of the recent supernovae type Ia data (SNIa), the
differential ages of passively evolving galaxies, and the Baryonic Acoustic
Oscillations (BAOs) traced by the Sloan Digital Sky Survey (SDSS), we put tight
constraints on the main cosmological parameters. Furthermore, we study the
linear matter fluctuation field of the above Liouville cosmological models. In
this framework, we compare the observed growth rate of clustering measured with
those predicted by the current Liouville models. Performing a chi^2 statistical
test we show that the Liouville cosmological model provides growth rates that
match sufficiently well with the observed growth rate. To further test the
viability of the models under study, we use the Press-Schechter formalism to
derive their expected redshift distribution of cluster-size halos that will be
provided by future X-ray and Sunyaev-Zeldovich cluster surveys. We find that
the Hubble flow differences between the Liouville and the LambdaCDM models
provide a significantly different halo redshift distribution, suggesting that
the models can be observationally distinguished.
