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

Abstract

The mass distribution of dark matter halos is a sensitive probe of primordial non-Gaussianity (NG). We derive an analytical formula of the halo mass function by perturbatively computing excursion set path-integrals for a non-Gaussian density field with non-vanishing skewness, fnl. We assume a stochastic barrier model which captures the main features of the ellipsoidal collapse of halos. Contrary to previous results based on extensions of the Press-Schechter formalism to NG initial conditions, we find that the non-spherical collapse of halos directly alter the signature of primordial NG. This points toward a potential degeneracy between the effect of primordial non-Gaussianity and that of non-linear halo collapse. The inferred mass function is found to be in remarkable agreement with N-body simulations of NG local type. Deviations are well within numerical uncertainties for all values of -80 < fNL^loc < 300 in the range of validity of the perturbative calculation. Moreover, the comparison with simulation results suggests that for fNL > 150 or fNL < -50 the non-linear collapse of halos, as described by our barrier model, strongly deviates from that of Gaussian initial conditions. This is not surprising since the effect of non-linear gravitational processes may be altered by initially large NG. Hence, in the lack of prior theoretical knowledge, halo collapse model parameters should be included in statistical halo mass function data analysis which aim to constrain the signature of primordial NG

We found a coding-bug in our numerical calculation of the function U3(S) which affected the comparison with non-Gaussian N-body simulations. Results change only quantitatively. 29 pages, 8 figures, typos corrected and added clarifications on the barrier model

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• The Hunt for Primordial Interactions in the Large Scale Structures of the Universe
• The Imprint of f(R) Gravity on Non-Linear Structure Formation
• Testing spherical evolution for modelling void abundances
• The mass function dependence on the dynamical state of dark matter haloes
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• Computation of the Halo Mass Function Using Physical Collapse Parameters: Application to Non-Standard Cosmologies
• The Effect of Local non-Gaussianity on the Matter Bispectrum at Small Scales
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• Excursion Set Theory for Correlated Random Walks
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