# Cosmology and Newtonian limit in a model of gravity with nonlocally interacting metrics

## TL;DR

This paper explores a nonlocal gravity model with two interacting metrics, analyzing its cosmological expansion, stability, and Solar System implications, revealing an effective dark energy behavior and small deviations from General Relativity.

## Contribution

It provides a detailed dynamical analysis of a nonlocal gravity model, showing the universe's effective equation of state approaches -1 and examining Solar System scale deviations.

## Key findings

- Effective equation of state tends to -1 regardless of model parameters.
- No stable critical points found in the dynamical system.
- Solar System tests show small deviations from GR depending on the nonlocality parameter.

## Abstract

We investigate the features of the cosmological expansion history described by a recent model of gravity characterised by two nonlocally interacting metrics. We perform a detailed analysis of the dynamical system formed by the field equations and we find no stable critical points at finite and infinite distance. Nonetheless, we show that even if the universe does not evolve towards a de Sitter attractor, the effective equation of state parameter $\omega_{\rm eff}$ always tends to $-1$, independently from the value of the free parameter $m^2$, which characterises the nonlocality of the theory. We also address the behaviour of gravity on Solar System scales and the growth of small cosmological fluctuations on small scales, in the quasi-static approximation. We find a post-Newtonian $\gamma$ parameter, a slip parameter and an effective, normalised gravitational coupling different from unity. These differences all depend on $m^2$ and are negligible if one consider the cosmological solution by which $m^2 \sim H_0^2$.