X-ray cluster constraints on non-Gaussianity

We report constraints on primordial non-Gaussianity from the abundance of Xray detected clusters. Our analytic prescription for adding non-Gaussianity to the cluster mass function takes into account moments beyond the skewness, and we demonstrate that those moments should not be ignored in most analyses of cluster data. We constrain the amplitude of the skewness for two scenarios that have different overall levels of non-Gaussianity, characterized by how amplitudes of higher cumulants scale with the skewness. We find that current data can constrain these one-parameter non-Gaussian models at a useful level, but are not sensitive to adding further details of the corresponding inflation scenarios. Combining cluster data with Cosmic Microwave Background constraints on the cosmology and power spectrum amplitude, we find the dimensionless skewness to be 10(3)M(3) = -1(-22)(+28) for one of our scaling scenarios, and 10(3)M(3) = -4 +/- 7 for the other. These are the first constraints on non-Gaussianity from Large Scale Structure that can be usefully applied to any model of primordial non-Gaussianity. The former constraint, when applied to the standard local i ansatz (where the n-th cumulant scales as M-n alpha M-3(n-2)), corresponds to f(NL)(local) = -3(-91)(+78). When applied to a model with a local-shape bispectrum but higher cumulants that scale as M-n, alpha M-3(n/3) (the second scaling scenario), the amplitude of the local-shape bispectrum is constrained to be f(NL)(local) = -14(-21)(+22). For this second scaling (which occurs in various well-motivated models of inflation), we also obtain strong constraints on the equilateral and orthogonal shapes of the bispectrum, f(NL)(equil) = -52(-79)(+85) and f(NL)(orth) = 63(-104)(+97). This sensitivity implies that cluster counts could be used to distinguish qualitatively different models for the primordial fluctuations that have identical bispectra.