Testing gravity with $E_G$: mapping theory onto observations

TL;DR

This paper derives the observational definition of the gravity test statistic $E_G$, analyzes uncertainties from theory and surveys, forecasts measurement errors, and evaluates its effectiveness for testing gravity with future data.

Contribution

It provides a complete derivation of $E_G$, assesses uncertainties, forecasts errors for upcoming surveys, and discusses its potential for testing modified gravity theories.

Findings

Theoretical uncertainties may dominate future measurements of $E_G$

Forecasted errors depend on survey combinations and parameters

Predictions of $E_G$ vary under different modified gravity models

Abstract

We present a complete derivation of the observationally motivated definition of the modified gravity statistic $E_G$. Using this expression, we investigate how variations to theory and survey parameters may introduce uncertainty in the general relativistic prediction of $E_G$. We forecast errors on $E_G$ for measurements using two combinations of upcoming surveys, and find that theoretical uncertainties may dominate for a futuristic measurement. Finally, we compute predictions of $E_G$ under modifications to general relativity in the quasistatic regime, and comment on the pros and cons of using $E_G$ to test gravity with future surveys.