Non-Gaussianity of the density distribution in accelerating universes   II:N-body simulations
  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. 
Takayuki Tatekawa and Shuntaro Mizuno