A generally covariant version of Erik Verlinde’s emergent gravity model is proposed. The Lagrangian constructed here allows an improved interpretation of the underlying mechanism. It suggests that de Sitter space is filled with a vector field that couples to baryonic matter and, by dragging on it, creates an effect similar to dark matter. We solve the covariant equation of motion in the background of a Schwarzschild space-time and obtain correction terms to the noncovariant expression. Furthermore, we demonstrate that the vector field can also mimic dark energy.

• Received 16 March 2017

DOI:https://doi.org/10.1103/PhysRevD.95.124018