Generalized Einstein theory on solar and galactic scales

We study a generalized Einstein theory with the following two criteria: (i) on the solar scale, it must be consistent with the classical tests of general relativity; (ii) on the galactic scale, the gravitational potential is a sum of Newtonian and Yukawa potentials so that it may explain the flat rotation curves of spiral galaxies. Under these criteria we find that such a generalized Einstein action must include at least one scalar field and one vector field as well as the quadratic term of the scalar curvature.