The initial shear field in models with primordial local non-Gaussianity and implications for halo and void abundances

TL;DR

This paper extends the initial shear field formulae to include local non-Gaussianity, analyzing its impact on halo and void abundances, and highlighting their potential to constrain primordial non-Gaussianity.

Contribution

It generalizes Doroshkevich's formulae for the initial shear field to non-Gaussian models and studies their effects on halo and void abundances.

Findings

Positive f_{nl} increases massive halo abundance

Positive f_{nl} decreases large void abundance

Void and halo abundances provide complementary constraints

Abstract

We generalize Doroshkevich's celebrated formulae for the eigenvalues of the initial shear field associated with Gaussian statistics to the local non-Gaussian f_{nl} model. This is possible because, to at least second order in f_{nl}, distributions at fixed overdensity are unchanged from the case f_{nl}=0. We use this generalization to estimate the effect of f_{nl}\ne 0 on the abundance of virialized halos. Halo abundances are expected to be related to the probability that a certain quantity in the initial fluctuation field exceeds a threshold value, and we study two choices for this variable: it can either be the sum of the eigenvalues of the initial deformation tensor (the initial overdensity), or its smallest eigenvalue. The approach based on a critical overdensity yields results which are in excellent agreement with numerical measurements. We then use these same methods to develop approximations describing the sensitivity of void abundances on f_{nl}. While a positive f_{nl} produces more extremely massive halos, it makes fewer extremely large voids. Its effect thus is qualitatively different from a simple rescaling of the normalisation of the density fluctuation field \sigma_8. Therefore, void abundances furnish complementary information to cluster abundances, and a joint comparison of both might provide interesting constraints on primordial non-Gaussianity.