Constraints on a non - gaussian ( χ 2 m ) CDM model

We consider constraints on the structure formation model based on non-gaussian fluctuations generated during inflation, which have χ 2 m 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 Ω 0 and lower bound of the non-gaussianity and the amplitude of the fluctuations. Using the abundance of clusters at z ∼ 0.6, for the spectrum parameterized by CDM shape parameter Γ = 0.23, we obtain upper bound of the density parameter Ω 0 ∼ 0.5 and lower bound of the amplitude σ 8 ∼ 0.7 and of the non-gaussianity T ∼ 2 (m ∼ 200) of fluctuations, where T represents the non-gaussianity of fluctuations (T = 1 for gaussian).