  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
non-covariant expression. Furthermore, we demonstrate that the vector field can
also mimic dark energy.
