Model-independent test for gravity using intensity mapping and galaxy clustering

We propose a novel method to measure the EG statistic from clustering alone. The EG statistic provides an elegant way of testing the consistency of General Relativity by comparing the geometry of the Universe, probed through gravitational lensing, with the motion of galaxies in that geometry. Current EG estimators combine galaxy clustering with gravitational lensing, measured either from cosmic shear or from CMB lensing. In this paper, we construct a novel estimator for EG, using only clustering information obtained from two tracers of the large-scale structure: intensity mapping and galaxy clustering. In this estimator, both the velocity of galaxies and gravitational lensing are measured through their impact on clustering. We show that with this estimator, we can suppress the contaminations that affect other EG estimators and consequently test the validity of General Relativity robustly. We forecast that with the coming generation of surveys like HIRAX and Euclid, we will measure EG with a precision of up to 7% (3.9% for the more futuristic SKA2).