# Testing nonlocal gravity with Lunar Laser Ranging

## TL;DR

This paper evaluates various nonlocal gravity models against Lunar Laser Ranging constraints on the variability of G, confirming the exclusion of RR and DW models while supporting the viability of the RT model.

## Contribution

The study provides a detailed analysis of nonlocal gravity models in light of Lunar Laser Ranging data, confirming the exclusion of RR and DW models and supporting RT model viability.

## Key findings

- RR model is ruled out by LLR constraints.
- DW model is ruled out due to ineffective screening.
- RT model remains consistent with phenomenological tests.

## Abstract

We study the impact of the limit on $|\dot{G}|/G$ from Lunar Laser Ranging on "nonlocal gravity", i.e. on models of the quantum effective action of gravity that include nonlocal terms relevant in the infrared, such as the "RR" and "RT" models proposed by our group, and the Deser-Woodard (DW) model. We elaborate on the analysis of Barreira et al. [1] and we confirm their findings that (under plausible assumptions such as the absence of strong backreaction from non-linear structures), the RR model is ruled out. We also show that the mechanism of "perfect screening for free" suggested for the DW model actually does not work and the DW model is also ruled out. In contrast, the RT model passes all phenomenological consistency tests and is still a viable candidate.