The observable $E_g$ statistics

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.