We report constraints on primordial non-Gaussianity from the abundance of X-ray 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 } \mathcal { M } _ { 3 } = -1 ^ { +24 } _ { -28 } for one of our scaling scenarios , and 10 ^ { 3 } \mathcal { M } _ { 3 } = -4 \pm 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 ansatz ( where the n -th cumulant scales as \mathcal { M } _ { n } \propto \mathcal { M } _ { 3 } ^ { n - 2 } ) , corresponds to f ^ { local } _ { NL } = -3 ^ { +78 } _ { -91 } .
When applied to a model with a local-shape bispectrum but higher cumulants that scale as \mathcal { M } _ { n } \propto \mathcal { M } _ { 3 } ^ { n / 3 } ( the second scaling scenario ) , the amplitude of the local-shape bispectrum is constrained to be f ^ { local* } _ { NL } = -14 ^ { +22 } _ { -21 } .
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 ^ { +85 } _ { -79 } and f _ { NL } ^ { orth } = 63 ^ { +97 } _ { -104 } .
This sensitivity implies that cluster counts could be used to distinguish qualitatively different models for the primordial fluctuations that have identical bispectra .