Galaxy number counts at second order in perturbation theory: a leading-order term comparison

TL;DR

This paper compares leading-order second perturbation theory calculations of galaxy number counts from different groups, highlighting differences mainly due to definitional ambiguities affecting second order terms.

Contribution

It provides a detailed comparison of independent second order perturbation theory calculations for galaxy counts, clarifying sources of discrepancies.

Findings

Differences mainly due to definitional ambiguities

Sign ambiguities lead to extra second order terms

Comparison enhances consistency in theoretical predictions

Abstract

The galaxy number density is a key quantity to compare theoretical predictions to the observational data from current and future Large Scale Structure surveys. The precision demanded by these Stage IV surveys requires the use of second order cosmological perturbation theory. Based on the independent calculation published previously, we present the result of the comparison with the results of three other groups at leading order. Overall we find that the differences between the different approaches lie mostly on the definition of certain quantities, where the ambiguity of signs results in the addition of extra terms at second order in perturbation theory.