  We explore the possibility of putting constraints on dark energy models with
statistical property of large scale structure in the non-linear region. In
particular, we investigate the $w$ dependence of non-Gaussianity of the
smoothed density distribution generated by the nonlinear dynamics. In order to
follow the non-linear evolution of the density fluctuations, we apply N-body
simulations based on $P^3 M$ scheme. We show that the relative difference
between non-Gaussianity of $w=-0.8$ model and that of $w=-1.0$ model is $0.67
%$ (skewness) and $1.2 %$ (kurtosis) for $R=8h^{-1}$ Mpc. We also calculate the
correspondent quantities for $R=2h^{-1}$ Mpc, $3.0 %$ (skewness) and $4.5 %$
(kurtosis), and the difference turn out to be greater, even though
non-linearity in this scale is so strong that the complex physical processes
about galaxy formation affect the galaxy distribution. From this, we can expect
that the difference can be tested by all sky galaxy surveys with the help of
mock catalogs created by selection functions, which suggests that
non-Gaussianity of the density distribution potentially plays an important role
for extracting information on dark energy.
