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\ndeviations from General Relativity on astrophysical and cosmological scales,\nnamely the parameterised post-Newtonian (PPN) formalism and the effective field\ntheory (EFT) of dark energy and modified gravity. These separate formalisms are\nsuccessfully applied to independently perform tests of gravity in their\nrespective regimes of applicability on vastly different length scales.\nNonlinear screening mechanisms indeed make it imperative to probe General\nRelativity across a wide range of scales. For a comprehensive interpretation of\nthe complementary measurements it is important to connect them to effectively\nconstrain the vast gravitational model space. We establish such a connection\nwithin the framework of Horndeski scalar-tensor theories restricted to a\nluminal propagation speed of gravitational waves. This is possible via the\nreconstruction of the family of linearly degenerate covariant Horndeski actions\nfrom the set of EFT functions and the subsequent derivation of the PPN\nparameters from the reconstructed theory. We outline the required conditions\nwhich ensure a reconstructed Horndeski model possesses a screening mechanism\nthat enables significant modifications on cosmological scales while respecting\nstringent astrophysical bounds. Employing a scaling method, we then perform the\ngeneral post-Newtonian expansion of the reconstructed models to derive their\nPPN parameters $\\gamma$ and $\\beta$ in their screened regimes.\n