Nonlocal metric formulations of MOND with sufficient lensing
  We demonstrate how to construct purely metric modifications of gravity which
agree with general relativity in the weak field regime appropriate to the solar
system, but which possess an ultra-weak field regime when the gravitational
acceleration becomes comparable to $a_0 \sim 10^{-10} {\rm m/s}^2$. In this
ultra-weak field regime, the models reproduce the MOND force without dark
matter and also give enough gravitational lensing to be consistent with
existing data. Our models are nonlocal and might conceivably derive from
quantum corrections to the effective field equations.
