Galaxy number counts at second order: an independent approach

TL;DR

This paper introduces a new independent method for calculating second-order relativistic galaxy number counts, improving theoretical precision for upcoming cosmological surveys and resolving previous disagreements at nonlinear levels.

Contribution

It provides an independent derivation of second-order relativistic galaxy number counts, including analytical expressions for observed redshift, angular diameter distance, and survey volume.

Findings

Results agree with previous linear-order calculations.

New analytical expressions for second-order effects.

Addresses discrepancies in nonlinear relativistic calculations.

Abstract

Next generation surveys will be capable of determining cosmological parameters beyond percent level. To match this precision, theoretical descriptions should look beyond the linear perturbations to approximate the observables in large scale structure. A quantity of interest is the Number density of galaxies detected by our instruments. This has been focus of interest recently, and several efforts have been made to explain relativistic effects theoretically, thereby testing the full theory. However, the results at nonlinear level from previous works are in disagreement. We present a new and independent approach to computing the relativistic galaxy number counts to second order in cosmological perturbation theory. We derive analytical expressions for the full second order relativistic observed redshift, for the angular diameter distance and for the volume spanned by a survey. Finally, we compare our results with previous works which compute the general distance-redshift relation, finding that our result is in agreement at linear order.