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arXiv · 0905.1706

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

Tsz Yan Lam·Ravi K. Sheth·Vincent Desjacques
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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 σ_8. Therefore, void abundances furnish complementary information to cluster abundances, and a joint comparison of both might provide interesting constraints on primordial non-Gaussianity.

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Tsz Yan Lam, Ravi K. Sheth, Vincent Desjacques. 2009-08-01. The initial shear field in models with primordial local non-Gaussianity and implications for halo and void abundances. https://doi.org/10.1111/j.1365-2966.2009.15363.x

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