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

Field equations and cosmology for a class of nonlocal metric models of MOND