Constraining Primordial Non-Gaussianity With the Abundance of High Redshift Clusters

Abstract

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 datasets 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 $Ω_m\simeq 0.3$ and are inconsistent with $Ω_m=1$ at the $2σ$ 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 two times as many peaks of height $3σ$ 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.