Using Cluster Abundances and Peculiar Velocities to Test the Gaussianity of the Cosmological Density Field

TL;DR

This work presents a framework to test the Gaussianity of the primordial density field by contrasting tail statistics from X-ray cluster abundances with rms fluctuations derived from peculiar velocities and redshift distortions, evaluating Gaussian versus texture PDFs. The authors extend Press-Schechter to non-Gaussian PDFs, relate cluster temperatures to initial perturbation scales via a Radius–Temperature relation, and account for formation epochs to infer $\eta_{10}$ values. A Bayesian comparison indicates Gaussian initial conditions are favored when aggregating rms data, though individual measurements (notably Willick 1997b) can favor textures depending on $\Omega_0$; cluster evolution constraints in particular tend to disfavour $\Omega_0=1$ Gaussian scenarios. Overall, the method provides a principled approach to discriminating initial density distributions on $\sim10\,h^{-1}$ Mpc scales, contingent on improved rms accuracy and higher-redshift cluster observations to break cosmological degeneracies.

Abstract

(Abridged) By comparing the frequency of typical events with that of unusual events, one can test whether the cosmological density distribution function is consistent with the normally made assumption of Gaussianity. To this end, we compare the consistency of the tail-inferred (from clusters) and measured values (from large-scale flows) of the rms level of mass fluctuations for two distribution functions: a Gaussian, and a texture (positively-skewed) PDF. Averaging the recent large-scale flow measurements, we find that observations of the rms and the tail at the 10 h^-1 Mpc scale disfavor a texture PDF at ~1.5 sigma in all cases. However, taking only the most recent measurement of the rms, that from Willick et al. (1997b), the comparison disfavors textures for low Omega_0=0.3, and disfavors Gaussian models if Omega_0=1 (again at ~1.5 sigma). Predictions for evolution of high temperature clusters can also be made for the models considered, and strongly disfavor Omega_0=1 in Gaussian models and marginally disfavor Omega_0=1 in texture models. Only Omega_0=0.3 Gaussian models are consistent with all the data considered.