Observational Tests of Nonlocal Gravity: Galaxy Rotation Curves and Clusters of Galaxies

A classical nonlocal generalization of Einstein's theory of gravitation has recently been developed via the introduction of a scalar causal "constitutive" kernel that must ultimately be determined from observational data. It turns out that the nonlocal aspect of gravity in this theory can simulate dark matter; indeed, in the Newtonian regime of nonlocal gravity, we recover the phenomenological Tohline-Kuhn approach to modified gravity. A simple generalization of the Kuhn kernel in the context of nonlocal general relativity leads to a two-parameter modified Newtonian force law that involves an additional repulsive Yukawa-type interaction. We determine the parameters of our nonlocal kernel by comparing the predictions of the theory with observational data regarding the rotation curves of spiral galaxies. The best-fitting stellar mass-to-light ratio turns out to be in agreement with astrophysical models; moreover, our results are consistent with the Tully-Fisher relation for spiral galaxies. Light deflection in nonlocal gravity is consistent with general relativity at Solar System scales, while beyond galactic scales an enhanced deflection angle is predicted that is compatible with lensing by the effective "dark matter". Furthermore, we extend our results to the internal dynamics of rich clusters of galaxies and show that the dynamical mass of the cluster obtained from nonlocal gravity is consistent with the measured baryonic mass.