The initial shear field in models with primordial local non-Gaussianity and implications for halo and void abundances |
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Authors: | Tsz Yan Lam Ravi K Sheth Vincent Desjacques |
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Institution: | Center for Particle Cosmology, University of Pennsylvania, 209 S. 33rd Street, Philadelphia, PA 19104, USA;Institute for the Physics and Mathematics of the Universe, University of Tokyo, Chiba 277-8582, Japan;Institute for Theoretical Physics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland |
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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. |
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Keywords: | methods: analytical large-scale structure of Universe |
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