Galaxy number counts to second order and their bispectrum

TL;DR

This paper calculates second-order galaxy number counts and their bispectrum using a geometric approach in the geodesic light-cone gauge, applicable to various dark energy and modified gravity models.

Contribution

It introduces an innovative geometric method to compute second-order galaxy counts without Einstein's equations, extending applicability to general dark energy and modified gravity models.

Findings

Numerical evaluation of the bispectrum contributions from density, redshift space distortion, and lensing.

First second-order calculation of galaxy counts in the geodesic light-cone gauge.

Framework applicable to a wide range of cosmological models.

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.