One Gravitational Potential or Two? Forecasts and Tests

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