# Parameterised Post-Newtonian Expansion in Screened Regions

## TL;DR

This paper extends the PPN formalism to include screening mechanisms in modified gravity theories by defining position-dependent parameters, and develops a method to compute these functions, applying it to specific models.

## Contribution

It introduces a general approach to incorporate screening effects into the PPN formalism and derives the PPN functions for cubic galileon and chameleon models.

## Key findings

- No deviations from GR in the Shapiro delay within screened regions.
- Derived all PPN functions for specific screening models.
- Developed an efficient method for post-Newtonian expansion in screened regimes.

## Abstract

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.