Constraining theories of gravity by fundamental plane of elliptical
  galaxies
  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.
