  We consider a class of nonlocal, pure-metric modified gravity models which
were developed to reproduce the Tully-Fisher relation without dark matter and
without changing the amount of weak lensing predicted by general relativity.
Previous work gave only the weak field limiting form of the field equations
specialized to a static and spherically symmetric geometry. Here we derive the
full field equations and specialize them to a homogeneous, isotropic and
spatially flat geometry. We also discuss the problem of fitting the free
function to reproduce the expansion history. Results are derived for models in
which the MOND acceleration a_0 ~ 1.2 x 10^{-10} m/s^{2} is a fundamental
constant and for the more phenomenologically interesting case in which the MOND
acceleration changes with the cosmological expansion rate.
