Constraints on a non-gaussian (${\chi }_m^2$) CDM model

Abstract

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.

7 pages, 3 figures, MNRAS in press

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