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 $a_0\approx 1.2\times 10^{-10}\mathrm{m}.{\mathrm{s}}^{-2}$ is a fundamental constant and for the more phenomenologically interesting case in which the MOND acceleration changes with the cosmological expansion rate.

• Received 2 May 2014
• Publisher error corrected 26 September 2014

DOI:https://doi.org/10.1103/PhysRevD.90.064038