X-ray Cluster Constraints on Non-Gaussianity
  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 1000*M3=-1+24-28 for one of our scaling scenarios, and
1000*M3=-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. When applied to the standard local ansatz,
the constraint corresponds to fNL=-3+78-91. When applied to a model with a
local-shape bispectrum but higher cumulants that are relatively more important,
the amplitude of the local-shape bispectrum is constrained to be fNL=-14+22-21.
This sensitivity implies that cluster counts could be used to distinguish
qualitatively different models for the primordial fluctuations that have
identical bispectra. (Abstract Abridged.)
