# Nonlinear stability in nonlocal gravity

## TL;DR

This paper proves the stability of Ricci-flat and maximally symmetric spacetimes in nonlocal gravity by mapping the problem to Einstein-Hilbert theory, ensuring ghost-free propagation and extending known Einstein gravity stability results.

## Contribution

It establishes a stability analysis framework for nonlocal gravity, showing it inherits Einstein gravity stability properties and remains ghost-free at all perturbative orders.

## Key findings

- Stability of Ricci-flat and maximally symmetric spacetimes in nonlocal gravity.
- Nonlocal gravity propagates only the graviton field, avoiding ghosts.
- Minkowski and de Sitter spacetimes are stable in this framework.

## Abstract

We address the stability issue of Ricci-flat and maximally symmetric spacetimes in nonlocal gravity to all perturbative orders in the gravitational perturbation. Assuming a potential at least cubic in curvature tensors but quadratic in the Ricci tensor, our proof consists on a mapping of the stability analysis in nonlocal gravity to the same problem in Einstein-Hilbert theory. One of the consequences is that only the graviton field can propagate and the theory is ghost-free at all perturbative orders. All the results known in Einstein gravity in vacuum with or without a cosmological constant can be exported to the case of nonlocal gravity: if a spacetime is stable at all perturbative orders in Einstein gravity, it is stable also in nonlocal gravity. Minkowski and de Sitter spacetimes are particular examples. We also study how the theory affects the propagation of gravitational waves in a cosmological background.