  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.
