# The observable $E_g$ statistics

## TL;DR

This paper introduces a new observable, $ ilde E_g$, that removes lensing contamination from the $E_g$ statistic using shear and galaxy clustering data, improving tests of modified gravity especially for future surveys.

## Contribution

The paper develops a method to eliminate lensing contributions from the $E_g$ statistic by combining shear and galaxy data, creating a bias- and scale-independent observable for linear scales.

## Key findings

- Corrections to $E_g$ are small for DES data.
- Corrections are substantial for future surveys like Euclid.
- The method is best suited for photometric surveys.

## Abstract

Recently Moradinezhad Dizgah & Durrer have shown that the $E_g$ statistics, useful to test theories of modified gravity, is plagued by additional scale and bias dependent lensing contributions. In this work we develop and illustrate a method to remove these lensing terms by using in addition to the galaxy clustering data also shear data and the correlations of shear and galaxy clustering. We introduce a truly observable statistics termed $\tilde E_g$ which conserves the properties of scale and bias independence on linear scales. The method discussed here is best adapted to photometric surveys. It is found that the corrections to the original $E_g$ statistics are small for the present DES data, but for future surveys of the quality of Euclid they are very substantial.