  Several independent cosmological tests have shown evidences that the energy
density of the Universe is dominated by a dark energy component, which cause
the present accelerated expansion. The large scale structure formation can be
used to probe dark energy models, and the mass function of dark matter haloes
is one of the best statistical tools to perform this study. We present here a
statistical analysis of mass functions of galaxies under a homogeneous dark
energy model, proposed in the work of Percival (2005), using an observational
flux-limited X-ray cluster survey, and CMB data from WMAP. We compare, in our
analysis, the standard Press-Schechter (PS) approach (where a Gaussian
distribution is used to describe the primordial density fluctuation field of
the mass function), and the PL (Power Law) mass function (where we apply a
nonextensive q-statistical distribution to the primordial density field). We
conclude that the PS mass function cannot explain at the same time the X-ray
and the CMB data (even at 99% confidence level), and the PS best fit dark
energy equation of state parameter is $\omega=-0.58$, which is distant from the
cosmological constant case. The PL mass function provides better fits to the
HIFLUGCS X-ray galaxy data and the CMB data; we also note that the $\omega$
parameter is very sensible to modifications in the PL free parameter, $q$,
suggesting that the PL mass function could be a powerful tool to constrain dark
energy models.
