Parameterised post-Newtonian formalism for the effective field theory of
  dark energy via screened reconstructed Horndeski theories
  We bring together two popular formalisms which generically parameterise
deviations from General Relativity on astrophysical and cosmological scales,
namely the parameterised post-Newtonian (PPN) formalism and the effective field
theory (EFT) of dark energy and modified gravity. These separate formalisms are
successfully applied to independently perform tests of gravity in their
respective regimes of applicability on vastly different length scales.
Nonlinear screening mechanisms indeed make it imperative to probe General
Relativity across a wide range of scales. For a comprehensive interpretation of
the complementary measurements it is important to connect them to effectively
constrain the vast gravitational model space. We establish such a connection
within the framework of Horndeski scalar-tensor theories restricted to a
luminal propagation speed of gravitational waves. This is possible via the
reconstruction of the family of linearly degenerate covariant Horndeski actions
from the set of EFT functions and the subsequent derivation of the PPN
parameters from the reconstructed theory. We outline the required conditions
which ensure a reconstructed Horndeski model possesses a screening mechanism
that enables significant modifications on cosmological scales while respecting
stringent astrophysical bounds. Employing a scaling method, we then perform the
general post-Newtonian expansion of the reconstructed models to derive their
PPN parameters $\gamma$ and $\beta$ in their screened regimes.
