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The Three-Point Correlation Function in Cosmology

Masahiro Takada·Bhuvnesh Jain
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Abstract

With the advent of high-quality surveys in cosmology the full three-point correlation function will be a valuable statistic for describing structure formation models. It contains information on cosmological parameters and detailed halo properties that cannot be extracted from the two-point correlation function. We use the halo clustering model to analytically calculate the three-point correlation function (3PCF) for general cosmological fields. We present detailed results for the configuration dependence of the 3-dimensional mass and galaxy distributions and the 2-dimensional cosmic shear field. We work in real space, where higher order correlation functions on small scales are easier to measure and interpret, but halo model calculations get rapidly intractable. Hence we develop techniques for accurate evaluations of the 1, 2 and 3-halo contributions to the 3PCF. The 3PCF violates the hierarchical ansatz in both its scale and configuration dependence. We study the behavior of the coefficient Q in the hierarchical expansion from large, quasilinear scales down to about 20 kpc. We find that the nonlinear 3PCF is sensitive to the halo profile of massive halos, especially its inner slope. We model the distribution of galaxies in halos and show that the 3PCF of red galaxies has a weaker configuration and scale dependence than the mass, while for blue galaxies it is very sensitive to the parameters of the galaxy formation model. The 3PCF from weak lensing on the other hand shows different scalings due to projection effects and a sensitivity to cosmological parameters.

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Masahiro Takada, Bhuvnesh Jain. 2003-01-27. The Three-Point Correlation Function in Cosmology. https://doi.org/10.1046/j.1365-8711.2003.06321.x

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