Constraining extended gravity models by S2 star orbits around the Galactic Centre

We investigate the possibility of explaining theoretically the observed deviations of S2 star orbit around the Galactic Centre using gravitational potentials derived from modified gravity models in the 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 the analytic functions f(R) and f(R, phi) where R is the Ricci scalar and phi is a scalar field whose meaning can be related to further gravitational degrees of freedom. We simulate the orbit of the S2 star around the Galactic Centre in f(R) (Yukawa-like) and f(R, phi) (Sanders-like) gravity potentials and compare it with New Technology Telescope/Very Large Telescope observations. Our simulations result in strong constraints on the range of gravity interaction. In the case of analytic functions f(R), we are not able to obtain reliable constraints on the derivative constants f(1) and f(2), because the current observations of the S2 star indicated that they may be highly mutually correlated. In the case of analytic functions f(R, phi), we are able to obtain reliable constraints on the derivative constants f(0), f(R), f(RR), f(phi), f(phi phi), and f(phi R). The approach we are proposing seems to be sufficiently reliable to constrain the modified gravity models from stellar orbits around the Galactic Centre.