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

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Abstract
Comparing the frequency of typical events with that of unusual events allows one to 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) probability distribution function (PDF). We find that if we average the recent large-scale flow measurements, observations of the rms and the tail at the 10 h-1 Mpc scale disfavor a texture PDF at ~1.5 σ in all cases. If we take the most recent measurement of the rms, that from Willick et al., the comparison disfavors textures for low Ω0 = 0.3, and disfavors Gaussian models if Ω0 = 1 (again at ~1.5 σ). Predictions for evolution of high-temperature clusters can also be made for the models considered, and, as is known (e.g., Henry), strongly disfavor Ω0 = 1 Gaussian models, while we find Ω0 = 1 marginally disfavored in texture models. Taking the suite of tests as a whole, and using all of the quoted data, it appears that textures are strongly disfavored and only the low-Ω0 Gaussian models are consistent with all the data considered. But given evidence for the internal inconsistency of the observational data, had we only used the recent Willick et al. results, the strength of our conclusion would have been reduced to the ~1 σ level.
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