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.
