  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 LCDM 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 LCDM model and the observed ones. We alleviate the
tension considering non-Gaussian primordial perturbations of the local type,
characterized by the parameter fnl and derive constraints on fnl arising from
the mere existence of these clusters. At the 95% confidence level, fnl>467 with
cosmological parameters fixed to their most likely WMAP5 values, or fnl > 123
(at 95% confidence) if we marginalize over WMAP5 parameters priors. In
combination with fnl constraints from Cosmic Microwave Background and halo
bias, this determination implies a scale-dependence of fnl at approx. 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 fnl>0 found here. In order to
reconcile these massive, high-z clusters with an fnl=0, their masses would need
to be systematically lowered by 1.5 sigma or the sigma8 parameter should be
approx. 3 sigma higher than CMB (and large-scale structure) constraints. The
existence of these objects is a puzzle: it either represents a challenge to the
LCDM paradigme or it is an indication that the mass estimates of clusters is
dramatically more uncertain than we think.
