Constraints on a non-gaussian ($χ_m^2$) CDM model

We consider constraints on the structure formation model based on non-gaussian fluctuations generated during inflation, which have $\chi_m^2$ distributions. Using three data sets, the abundance of the clusters at $z=0$, at moderate $z$ and the correlation length, we show constraints on the non-gaussianity and the amplitude of fluctuations and the density parameter can be obtained. We obtain upper bound of $\Omega_0$ and lower bound of the non-gaussianity and the amplitude of the fluctuations. Using the abundance of clusters at $z \sim 0.6$, for the spectrum parameterized by CDM shape parameter $\Gamma=0.23$, we obtain upper bound of the density parameter $\Omega_0 \sim 0.5$ and lower bound of the amplitude $\sigma_8 \sim 0.7$ and of the non-gaussianity $T \sim 2$ $(m \sim 200)$ of fluctuations, where $T$ represents the non-gaussianity of fluctuations (T=1 for gaussian).