  According to recent observations, the existence of the dark energy has been
considered. Even though we have obtained the constraint of the equation of the
state for dark energy ($p = w \rho$) as $-1 \le w \le -0.78$ by combining WMAP
data with other astronomical data, in order to pin down $w$, it is necessary to
use other independent observational tools. For this purpose, we consider the
$w$ dependence of the non-Gaussianity of the density distribution generated by
nonlinear dynamics. To extract the non-Gaussianity, we follow a semi-analytic
approach based on Lagrangian linear perturbation theory, which provides an
accurate value for the quasi-nonlinear region. From our results, the difference
of the non-Gaussianity between $w = -1$ and $w= -0.5$ is about 4% while that
between $w = -1$ and $w= -0.8$ is about $0.9 %$. For the highly non-linear
region, we estimate the difference by combining this perturbative approach with
N-body simulation executed for our previous paper. From this, we can expect the
difference to be more enhanced in the low-$z$ region, which suggests that the
non-Gaussianity of the density distribution potentially plays an important role
for extracting the information of dark energy.
