Possible effects of Hybrid Gravity on stellar kinematics in elliptical galaxies

We use the Fundamental Plane of Elliptical Galaxies to constrain the so-called Hybrid Gravity, a modified theory of gravity where General Relativity is improved by further degrees of freedom of metric-affine Palatini formalism of $f(\cal R)$ gravity. Because the Fundamental Plane is connected to the global properties of elliptical galaxies, it is possible to obtain observational constraints on the parameters of Hybrid Gravity in the weak field limit. We analyze also the velocity distribution of elliptical galaxies comparing our theoretical results in the case of Hybrid Gravity with astronomical data for elliptical galaxies. In this way, we are able to constrain the Hybrid Gravity parameters $m_\phi$ and $\phi_0$. We show that the Fundamental Plane, i.e. $v_c/\sigma$ relations, can be used as a standard tool to probe different theories of gravity in the weak field limit. We conclude that Hybrid Gravity is able to explain elliptical galaxies with different stellar kinematics without the dark matter hypothesis.