We show that fundamental plane of elliptical galaxies can be used to obtain observational constraints on metric theories of gravity. Being it connected to global properties of ellipticals, it can fix parameters of modified gravity. Specifically, we use fundamental plane to constrain modified theories of gravity with Yukawa-like corrections which commonly emerge in the post-Newtonian limit. After giving examples on how these corrections are derived, we first analyze the velocity distribution of elliptical galaxies comparing theoretical results of modified gravity with Yukawa-like corrections with astronomical data. According to these results, it is possible to constrain the parameters of the corrections discriminating among classes of models compatible with astronomical observations. We conclude that fundamental plane can be used as a standard tool to probe different theories of gravity in the weak field limit.

我们表明，椭圆星系的基本平面可用于获得重力度量理论的观测约束。由于它与椭圆的全局特性有关，因此可以固定修改后的重力参数。具体来说，我们使用基本平面来约束修正后的重力理论，并采用类似于Yukawa的修正，这种修正通常出现在后牛顿极限中。在给出了如何得出这些修正的示例之后，我们首先分析了椭圆星系的速度分布，将修正重力的理论结果与类似Yukawa的修正和天文数据进行了比较。根据这些结果，可以约束与天文观测兼容的模型类别之间区别的校正参数。