Primordial non-Gaussianity from the covariance of galaxy cluster counts

It has recently been proposed that the large-scale bias of dark matter halos depends sensitively on primordial non-Gaussianity of the local form. In this paper we point out that the strong scale dependence of the non-Gaussian halo bias imprints a distinct signature on the covariance of cluster counts. We find that using the full covariance of cluster counts results in improvements on constraints on the non-Gaussian parameter f_NL of three (one) orders of magnitude relative to cluster counts (counts + clustering variance) constraints alone. We forecast f_NL constraints for the upcoming Dark Energy Survey in the presence of uncertainties in the mass-observable relation, halo bias, and photometric redshifts. We find that the DES can yield constraints on non-Gaussianity of sigma(f_NL) ~ 1-5 even for relatively conservative assumptions regarding systematics. Excess of correlations of cluster counts on scales of hundreds of megaparsecs would represent a smoking gun signature of primordial non-Gaussianity of the local type.