Observed galaxy number counts on the lightcone up to second order: I. Main result

TL;DR

This paper derives the second-order galaxy number overdensity in redshift space, incorporating all relativistic effects on the light cone, crucial for precise cosmological measurements and understanding non-Gaussianity.

Contribution

It provides the first comprehensive second-order relativistic galaxy number count formula including all effects from observing on the light cone.

Findings

Includes all relativistic effects up to second order.

Accounts for lensing, Sachs-Wolfe, and velocity contributions.

Facilitates more accurate cosmological parameter estimation.

Abstract

We present the galaxy number overdensity up to second order in redshift space on cosmological scales for a concordance model. The result contains all general relativistic effects up to second order that arise from observing on the past light cone, including all redshift effects, lensing distortions from convergence and shear, and contributions from velocities, Sachs-Wolfe, integrated SW and time-delay terms. This result will be important for accurate calculation of the bias on estimates of non-Gaussianity and on precision parameter estimates, introduced by nonlinear projection effects.