Implications of multiple high-redshift galaxy clusters

To date, 14 high-redshift (z > 1.0) galaxy clusters with mass measurements have been observed, spectroscopically confirmed, and are reported in the literature. These objects should be exceedingly rare in the standard Lambda cold dark matter (Lambda CDM) model. We conservatively approximate the selection functions of these clusters' parent surveys and quantify the tension between the abundances of massive clusters as predicted by the standard Lambda CDM model and the observed ones. We alleviate the tension, considering non-Gaussian primordial perturbations of the local type, characterized by the parameter f(NL), and derive constraints on f(NL) arising from the mere existence of these clusters. At the 95% confidence level, f(NL) > 467, with cosmological parameters fixed to their most likely WMAP5 values, or f(NL) greater than or similar to 123 (at 95% confidence) if we marginalize over prior WMAP5 parameters. In combination with f(NL) constraints from cosmic microwave background and halo bias, this determination implies a scale dependence of f(NL) at similar or equal to 3 sigma. Given the assumptions made in the analysis, we expect any future improvements to the modeling of the non-Gaussian mass function, survey volumes, or selection functions to increase the significance of f(NL) > 0 found here. In order to reconcile these massive, high-z clusters with f(NL) = 0, their masses would need to be systematically lowered by 1.5 sigma, or the sigma(8) parameter should be similar to 3 sigma higher than cosmic microwave background (and large-scale structure) constraints. The existence of these objects is a puzzle: it either represents a challenge to the Lambda CDM paradigm or it is an indication that the mass estimates of clusters are dramatically more uncertain than we think.