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.
