Dark matter and modified gravity: Einstein clusters from a non-minimally coupled vector field

Abstract

We show that a vector field non-minimally coupled to gravity reproduces exactly the dynamics of an Einstein cluster -- a large ensemble of non-interacting particles moving on circular geodesics under their collective gravitational field. Since Einstein clusters are known to be able to account for flat galactic rotation curves, our results suggest that such rotation curves may arise as a manifestation of modified gravity.

5 pages: V2: expanded discussion and new title