Estimating fNL and gNL from massive high-redshift galaxy clusters

There are observations of at least 14 high-redshift massive galaxy clusters, which have an extremely small probability with a purely Gaussian initial curvature perturbation. Here we revisit the estimation of the contribution of non-Gaussianities to the cluster mass function and point out serious problems that have resulted from the application of the mass function out of the range of its validity. We remedy the situation and show that the values of fNL previously claimed to completely reconcile (i.e. at ∼ 100% confidence) the existence of the clusters with ΛCDM are unphysically small. However, for WMAP cosmology and at 95% confidence, we arrive at the limit fNL∼>411, which is similar to previous estimates. We also explore the possibility of a large gNL as the reason for the observed excess of the massive galaxy clusters. This scenario, gNL > 2 × 106, appears to be in more agreement with CMB and LSS limits for the non-Gaussianity parameters and could also provide an explanation for the overabundance of large voids in the early universe