Constraining Extended Gravity Models by S2 star orbits around the Galactic Centre

TL;DR

This paper tests extended gravity models against S2 star orbit data near the Galactic Centre, constraining model parameters and demonstrating the potential of stellar orbits to limit modified gravity theories.

Contribution

It introduces a method to constrain extended gravity models using S2 star orbit observations, providing new bounds on model parameters without dark matter assumptions.

Findings

Strong constraints on gravity interaction range from S2 star data.

Limited constraints on $f(R)$ model parameters due to parameter correlation.

Reliable constraints obtained for parameters in $f(R,\, ext{phi})$ models.

Abstract

We investigate the possibility to explain theoretically the observed deviations of S2 star orbit around the Galactic Centre using gravitational potentials derived from modified gravity models in absence of dark matter. To this aim, an analytic fourth-order theory of gravity, non-minimally coupled with a massive scalar field is considered. Specifically, the interaction term is given by 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 S2 star around the Galactic Centre in $f(R)$ (Yukawa-like) and $f(R,\phi)$ (Sanders-like) gravity potentials and compare it with NTT/VLT 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 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 Galactic Centre.