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


Lam, T Y; Sheth, R K; Desjacques, V (2009). The initial shear field in models with primordial local non-Gaussianity and implications for halo and void abundances. Monthly Notices of the Royal Astronomical Society, 399(3):1482-1494.

Abstract

We generalize the Doroshkevich's celebrated formulae for the eigenvalues of the initial shear field associated with Gaussian statistics to the local non-Gaussian fnl model. This is possible because, to at least second order in fnl , distributions at fixed overdensity are unchanged from the case fnl= 0 . We use this generalization to estimate the effect of fnl≠ 0 on the abundance of virialized haloes. 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 fnl . While a positive fnl produces more extremely massive haloes, it makes fewer extremely large voids. Its effect thus is qualitatively different from a simple rescaling of the normalization of the density fluctuation field σ8. Therefore, void abundances furnish complementary information to cluster abundances, and a joint comparison of both might provide interesting constraints on primordial non-Gaussianity.

We generalize the Doroshkevich's celebrated formulae for the eigenvalues of the initial shear field associated with Gaussian statistics to the local non-Gaussian fnl model. This is possible because, to at least second order in fnl , distributions at fixed overdensity are unchanged from the case fnl= 0 . We use this generalization to estimate the effect of fnl≠ 0 on the abundance of virialized haloes. 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 fnl . While a positive fnl produces more extremely massive haloes, it makes fewer extremely large voids. Its effect thus is qualitatively different from a simple rescaling of the normalization of the density fluctuation field σ8. 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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute for Computational Science
Dewey Decimal Classification:530 Physics
Uncontrolled Keywords:methods: analytical; large-scale structure of Universe
Language:English
Date:November 2009
Deposited On:26 Feb 2010 15:00
Last Modified:05 Apr 2016 13:56
Publisher:Wiley-Blackwell
ISSN:0035-8711
Funders:Swiss National Foundation [200021-116696/1]
Additional Information:The attached file is a preprint (accepted version) of an article published in Monthly Notices of the Royal Astronomical Society. The definitive version is available at www3.interscience.wiley.com
Publisher DOI:10.1111/j.1365-2966.2009.15363.x
Related URLs:http://arxiv.org/abs/0905.1706
Permanent URL: http://doi.org/10.5167/uzh-30859

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