Nonlocal Metric Realizations of MOND

I discuss relativistic extensions of MOND in which the metric couples normally to matter. I argue that MOND might be a residual effect from the vacuum polarization of infrared gravitons produced during primordial inflation. If so, MOND corrections to the gravitational field equations would be nonlocal. Nonocality also results when one constructs metric field equations which reproduce the Tully-Fisher relation, along with sufficient weak lensing. I give the full field equations for the simplest class of models, and I specialize these equations to the geometries relevant for cosmology. I conclude by sketching the direction of future studies.