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We show that fundamental plane of elliptical galaxies can be used to obtainobservational constraints on metric theories of gravity. Being it connected toglobal properties of ellipticals, it can fix parameters of modified gravity.Specifically, we use fundamental plane to constrain modified theories ofgravity with Yukawa-like corrections which commonly emerge in thepost-Newtonian limit. After giving examples on how these corrections arederived, we first analyze the velocity distribution of elliptical galaxiescomparing theoretical results of modified gravity with Yukawa-like correctionswith astronomical data. According to these results, it is possible to constrainthe parameters of the corrections discriminating among classes of modelscompatible with astronomical observations. We conclude that fundamental planecan be used as a standard tool to probe different theories of gravity in theweak field limit.

Constraining theories of gravity by fundamental plane of elliptical galaxies