The Lagrangian description of perfect fluids and modified gravity with
  an extra force
  We revisit the issue of the correct Lagrangian description of a perfect fluid
(pressure versus minus energy density) in relation with modified gravity
theories in which galactic luminous matter couples nonminimally to the Ricci
scalar. These Lagrangians are only equivalent when the fluid couples minimally
to gravity and not otherwise; in the presence of nonminimal coupling they give
rise to two distinct theories with different predictions.
