Higher order relativistic galaxy number counts: dominating terms

TL;DR

This paper reviews and derives the dominant second-order relativistic galaxy number counts on sub-horizon scales, extends the derivation to third order, and discusses their relevance for 1-loop power spectrum calculations.

Contribution

It provides a comprehensive derivation of dominant second and third order galaxy number counts and compares these with existing literature, enabling improved theoretical modeling.

Findings

Derived the dominant second-order terms for galaxy counts on sub-horizon scales.

Extended the derivation to third order for 1-loop power spectrum computations.

Compared new results with previous literature to clarify differences.

Abstract

We review the number counts to second order concentrating on the terms which dominate on sub horizon scales. We re-derive the result for these terms and compare it with the different versions found in the literature. We generalize our derivation to higher order terms, especially the third order number counts which are needed to compute the 1-loop contribution to the power spectrum.