Nonlocal gravity is the recent classical nonlocal generalization of Einstein ’ s theory of gravitation in which the past history of the gravitational field is taken into account .
In this theory , nonlocality appears to simulate dark matter .
The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for “ isolated ” astronomical systems in virial equilibrium at the present epoch are investigated .
In particular , for a sufficiently isolated nearby galaxy in virial equilibrium , the galaxy ’ s baryonic diameter \mathcal { D } _ { 0 } —namely , the diameter of the smallest sphere that completely surrounds the baryonic system at the present time—is predicted to be larger than the effective dark matter fraction f _ { DM } times a universal length that is the basic nonlocality length scale \lambda _ { 0 } \approx 3 \pm 2 kpc .