Dark matter according to the tensor-four-scalars theory

Massive gravity previously constructed as the spin-2 quantum gauge theory leads in the mass zero limit to a modification of general relativity. As a relic from the massive theory a vector field v survives which couples to the metric only. However, the coupling does not involve covariant derivatives so that v must be considered as 4 scalar fields. We analyse the static, spherically symmetric solutions of this theory. From the corresponding geodesics we find the circular velocity profile. Interpreting this as coming from a dark density profile, the theory predicts a flat density core for r going to 0. But the dark density profile is not universal.