Constraining Primordial Non‐Gaussianity with the Abundance of High‐Redshift Clusters

We show how observations of the evolution of the galaxy cluster number abundance can be used to constrain primordial non-Gaussianity in the universe. We carry out a maximum likelihood analysis incorporating a number of current data sets and accounting for a wide range of sources of systematic error. Under the assumption of Gaussianity, the current data prefer a universe with matter density Ω m ≃ 0.3 and are inconsistent with Ω m = 1 at the 2 σ level. If we assume Ω m = 1, the predicted degree of cluster evolution is consistent with the data for non-Gaussian models where the primordial fluctuations have at least twice as many peaks of height 3 σ or more as a Gaussian distribution does. These results are robust to almost all sources of systematic error considered: in particular, the Ω m = 1 Gaussian case can only be reconciled with the data if a number of systematic effects conspire to modify the analysis in the right direction. Given an independent measurement of Ω m , the techniques described here represent a powerful tool with which to constrain non-Gaussianity in the primordial universe, independent of specific details of the non-Gaussian physics. We discuss the prospects and strategies for improving the constraints with future observations.