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The metric of a perturbed Robertson-Walker spacetime is characterized bythree functions: a scale-factor giving the expansion history and two potentialswhich generalize the single potential of Newtonian gravity. The Newtonianpotential induces peculiar velocities and, from these, the growth of matterfluctuations. Massless particles respond equally to the Newtonian potential andto a curvature potential. The difference of the two potentials, called thegravitational slip, is predicted to be very small in general relativity but canbe substantial in modified gravity theories. The two potentials can bemeasured, and gravity tested on cosmological scales, by combining weakgravitational lensing or the Integrated Sachs-Wolfe effect with galaxy peculiarvelocities or clustering.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

One Gravitational Potential or Two? Forecasts and Tests