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 $z=0$, moderate $z$ and the correlation length, we show that constraints on the non-Gaussianity and the amplitude of fluctuations and the density parameter can be obtained. We obtain an upper bound for $\Omega_m$ and a lower bound for the non-Gaussianity and the amplitude of the fluctuations. Using the abundance of clusters at $z \sim 0.6$, for the spectrum parameterized by cold dark matter (CDM) shape parameter $\Gamma=0.23$, we obtain an upper bound for the density parameter $\Omega_m \sim 0.5$ and lower bounds for the amplitude $\sigma_8 \sim 0.7$ and for the non-Gaussianity of fluctuations $G \sim 2$ $(m \sim 200)$, where G=1 for Gaussian.