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 \(f(\mathcal R)\) 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.

我们使用椭圆星系的基本平面来约束所谓的混合重力，这是一种改良的重力理论，其中广义相对论通过\（f（\ mathcal R）\）重力的度量仿射Palatini形式主义的进一步自由度得到了改善。由于基本面与椭圆星系的整体性质有关，因此可以在弱视场范围内获得对混合重力参数的观测约束。我们还分析了椭圆星系的速度分布，并将混合重力情况下的理论结果与椭圆星系的天文数据进行了比较。这样，我们就可以约束混合重力参数\（m_ \ phi \）和\（\ phi _0 \）。我们证明了基本平面，即\（v_c / \ sigma \）关系，可以用作探测弱场极限中不同引力理论的标准工具。我们得出的结论是，混合引力能够在没有暗物质假设的情况下解释具有不同恒星运动学的椭圆星系。