Screenings in Modified Gravity: a perturbative approach
  We present a formalism to study screening mechanisms in modified theories of
gravity via perturbative methods in different cosmological scenarios. We
consider Einstein frame posed theories that are recast as Jordan frame
theories, where a known formalism is employed, though the resulting
non-linearities of the Klein-Gordon equation acquire an explicit coupling
between matter and the scalar field, which is not present in Jordan frame
theories. The obtained growth functions are then separated in screening and
non-screened contributions to facilitate its analysis. This allows us to
compare several theoretical models and to recognize patterns which can be used
to differentiate models and their screening mechanisms. In particular, we find
anti-screening features in the Symmetron model. In opposition, chameleon type
theories, both in the Jordan and in the Einstein frame, always present a
screening behaviour. Up to third order in perturbation, we find no
anti-screening behaviour in theories with a Vainshtein mechanism, such as the
DGP and the cubic Galileon.
