2009/05/31 by Tsz Yan Lam, Ravi K. Sheth, Vincent Desjacques
Physics and Astronomy · #Astronomy #Astronomy and Astrophysical Research #Astrophysics #Cosmic microwave background #Cosmology and Gravitation Theories #Field (mathematics) #Galaxies: Formation, Evolution, Phenomena #Galaxy #Halo #Non-Gaussianity #Physics #Quantum mechanics #Shear (geology) #Void (composites) #astro-ph.CO
paper · pdf · doi:10.1111/j.1365-2966.2009.15363.x
16 pages, 8 figures, match version accepted by MNRAS
arxiv created 2009/08/01 · openalex publication_date 2009/09/03 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.