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.

38 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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Cited by in corpus (7)

• Non-Gaussianities due to Relativistic Corrections to the Observed Galaxy Bispectrum
• A general relativistic signature in the galaxy bispectrum: the local effects of observing on the lightcone
• Lensing in the Geodesic Light-Cone coordinates and its (exact) illustration to an off-center observer in Lemaître-Tolman-Bondi models
• General relativistic corrections and non-Gaussianity in large scale structure
• Exact non-linear equations for cosmological perturbations
• Lensing smoothing of BAO wiggles
• Non-linear power spectra in the synchronous gauge