Parameterised Post-Newtonian Expansion in Screened Regions

The parameterised post-Newtonian (PPN) formalism has enabled stringent tests of static weak-field gravity in a theory-independent manner. Here we incorporate screening mechanisms of modified gravity theories into the framework by introducing an effective gravitational coupling and defining the PPN parameters as functions of position. To determine these functions we develop a general method for efficiently performing the post-Newtonian expansion in screened regimes. For illustration, we derive all the PPN functions for a cubic galileon and a chameleon model. We also analyse the Shapiro time delay effect for these two models and find no deviations from General Relativity insofar as the signal path and the perturbing mass reside in a screened region of space.