Galaxy rotation curves in $f(R,\phi)$-gravity

We investigate the possibility to explain theoretically the galaxy rotation curves by a gravitational potential in total absence of dark matter. To this aim an analytic fourth-order theory of gravity, nonminimally coupled with a massive scalar field is considered. Specifically, the interaction term is given by an analytic function $f(R,\phi)$ where $R$ is the Ricci scalar and $\phi$ is the scalar field. The gravitational potential is generated by a point-like source and compared with the so called Sanders's potential that can be exactly reproduced in this case. This result means that the problem of dark matter in spiral galaxies could be fully addressed by revising general relativity at galactic scales and requiring further gravitational degrees of freedom instead of new material components that have not been found out up to now.