# Will-Nordtvedt PPN formalism applied to renormalization group extensions of general relativity

## TL;DR

This paper applies the comprehensive Will-Nordtvedt PPN formalism to analyze RG-based extensions of general relativity, providing stronger bounds and considering environmental effects like the External Potential Effect.

## Contribution

It extends previous PPN analyses by using the full Will-Nordtvedt formalism, offering more precise bounds on RG-based gravity models and exploring environmental effects such as the EPE.

## Key findings

- Stronger bounds on RG effects in gravity models.
- Identification of a RG realization unaffected by the EPE.
- Implications for Solar System tests of modified gravity.

## Abstract

Here we apply the full Will-Nordtvedt version of the Parameterized Post-Newtonian (PPN) formalism to a class of General Relativity extensions that are based on nontrivial renormalization group (RG) effects at large scales. We focus on a class of models in which the gravitational coupling constant $G$ is correlated with the Newtonian potential. A previous PPN analysis considered a specific realization of the RG effects, and only within the Eddington-Robertson-Schiff version of the PPN formalism, which is a less complete and robust PPN formulation. Here we find stronger, more precise bounds, and with less assumptions. We also consider the External Potential Effect (EPE), which is an effect that is intrinsic to this framework and depends on the system environment (it has some qualitative similarities to the screening mechanisms of modified gravity theories). We find a single particular RG realization that is not affected by the EPE. Some physical systems have been pointed out as candidates for measuring the possible RG effects in gravity at large scales, for any of them the Solar System bounds need to be considered.