Constraints on a non-Gaussian χm2 cold dark matter model

We consider constraints on the structure formation model based on non-Gaussian fluctuations generated during inflation, which have χₘ² 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 Ωₘ and a lower bound for the non-Gaussianity and the amplitude of the fluctuations. Using the abundance of clusters at z ~ 0.6, for the spectrum parameterized by cold dark matter (CDM) shape parameter Γ=0.23, we obtain an upper bound for the density parameter Ωₘ ~ 0.5 and lower bounds for the amplitude σ₈ ~ 0.7 and for the non-Gaussianity of fluctuations G ~ 2 (m ~ 200), where G=1 for Gaussian.