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We consider possible signatures for the so called {\it hybrid gravity} withinthe Galactic Central Parsec. This modified theory of gravity consists of asuperposition of the metric Einstein-Hilbert Lagrangian with an $f(R)$ termconstructed {\it \`{a} la Palatini} and can be easily reduced to an equivalentscalar-tensor theory. Such an approach is introduced in order to cure theshortcomings related to $f(R)$ gravity, in general formulated either in metricor in metric-affine frameworks. Hybrid gravity allows to disentangle thefurther gravitational degrees of freedom with respect to those of standardGeneral Relativity. The present analysis is based on the S2 star orbitalprecession around the massive compact dark object at the Galactic Centre wherethe simulated orbits in hybrid modified gravity are compared with astronomicalobservations. These simulations result with constraints on the range of hybridgravity interaction parameter $\phi_0$, showing that in the case of S2 star itis between -0.0009 and -0.0002. At the same time, we are also able to obtainthe constraints on the effective mass parameter $m_{\phi}$, and found that itis between -0.0034 and -0.0025 AU$^{-1}$ for S2 star. Furthermore, the hybridgravity potential induces precession of S2 star orbit in the same direction asGeneral Relativity. In previous papers, we considered other types of extendedgravities, like metric power law $f(R)\propto R^n$ gravity, inducing Yukawa andSanders-like gravitational potentials, but it seems that hybrid gravity is thebest among these models to explain different gravitational phenomena atdifferent astronomical scales.

Probing hybrid modified gravity by stellar motion around Galactic Centre