Galaxy number counts to second order and their bispectrum

Abstract

We determine the number counts to second order in cosmological perturbation theory in the Poisson gauge and allowing for anisotropic stress. The calculation is performed using an innovative approach based on the recently proposed "geodesic light-cone" gauge. This allows us to determine the number counts in a purely geometric way, without using Einstein's equation. The result is valid for general dark energy models and (most) modified gravity models. We then evaluate numerically the relevant contributions to the number counts bispectrum. In particular we consider the terms involving the density, redshift space distortion and lensing.

arXiv comment38 pages, 4 figures. Version published in JCAP including an erratum accepted for publication which corrects some errors in the final form of the equations

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