Non-Gaussian Halo Mass Function and Non-Spherical Halo Collapse: Theory vs. Simulations

The statistical properties of the cosmic matter distribution carry unique information on the quantum mechanical processes that during the early inflationary era have generated the spectrum of primordial inhomogeneities. The standard model of inflation predicts a nearly Gaussian spectrum of primordial density fluctuations, while competing scenarios predict deviations from Gaussian statistics. Such deviations can be tested through a variety of observational probes among which the number counts of the most massive halos in the Universe is believed to be one of the most sensitive. Ixandra Achitouv and Pier Stefano Corasaniti have investigated how the imprint of the non-spherical gravitational collapse of dark matter, which leads to the formation of halos, alters the signature of primordial non-Gaussianity on the halo mass function. To this end the researchers have derived an analytical formulae using a path-integral approach to predict the halo counting statistics for a given type of primordial non-Gaussianity (PNG), while assuming simple model of the halo formation process which captures the main features of the non-spherical collapse of dark matter. The result of the computation shows that the PNG signal is entangled to that of the non-linear gravitational collapse, thus potentially diluted than previously thought. The authors found an unprecedented agreement comparing the analytical prediction against non-Gaussian N-body simulation results. More importantly, the comparative analysis indicated that deviations from the spherical collapse prediction increases for larger non-Gaussinity. In other words the larger is the deviation from non-Gaussian statistics and the greater is the departure from a simple spherical collapse model of halo formation. This explain why alternative approaches that have attempt to compute the non-Gaussian halo mass function require introducing an ad-hoc tuning parameter to recover non-Gaussian N-body simulation results.

The results have been published on the Journal of Cosmology and Astroparticle Physics.