A discriminating probe of gravity at cosmological scales

The standard cosmological model is based on general relativity and includes dark matter and dark energy. An important prediction of this model is a fixed relationship between the gravitational potentials responsible for gravitational lensing and the matter overdensity. Alternative theories of gravity often make different predictions for this relationship. We propose a set of measurements which can test the lensing/matter relationship, thereby distinguishing between dark energy/matter models and models in which gravity differs from general relativity. Planned optical, infrared and radio galaxy and lensing surveys will be able to measure $E_G$, an observational quantity whose expectation value is equal to the ratio of the Laplacian of the Newtonian potentials to the peculiar velocity divergence, to percent accuracy. We show that this will easily separate alternatives such as $\Lambda$CDM, DGP, TeVeS and $f(R)$ gravity.