Lensing corrections to the $E_g(z)$ statistics from large scale structure

TL;DR

This paper investigates how lensing effects, often ignored, significantly influence the $E_g(z)$ statistics used to test gravity theories, especially at high redshifts, challenging its reliability.

Contribution

It quantifies the impact of lensing corrections on $E_g$ statistics and highlights their scale and bias dependence, questioning the statistic's robustness.

Findings

Lensing effects significantly alter $E_g$ measurements at high redshift.

Neglecting lensing introduces substantial errors in $E_g$ spectra.

Including lensing makes $E_g$ scale and bias-dependent.

Abstract

We study the impact of the often neglected lensing contribution to galaxy number counts on the $E_g$ statistics which is used to constrain deviations from GR. This contribution affects both the galaxy-galaxy and the convergence-galaxy spectra, while it is larger for the latter. At higher redshifts probed by upcoming surveys, neglecting this term induces a substantial error in the spectra and therefore on the $E_g$ statistics which is constructed from the combination of the two. Moreover, including it, renders the $E_g$ statistics scale and bias-dependent and hence puts into question its very objective.