Newtonian limit of nonlocal cosmology

TL;DR

This paper investigates the implications of $f(R/ox)$ gravity models on solar system tests and cosmic structure formation, revealing minor modifications to gravitational modes and establishing constraints consistent with observations.

Contribution

It provides a detailed analysis of the Newtonian limit and perturbation modes in $f(R/ox)$ gravity, highlighting the presence of new scalar degrees of freedom and their stability.

Findings

Tensor and vector modes are only slightly modified.

Two new scalar degrees of freedom are present.

The models are consistent with solar system and cosmological observations.

Abstract

We study the consequences of the $f(R/\Box)$ gravity models for the Solar system and the large scale structure of the universe. The spherically symmetric solutions can be used to obtain bounds on the constant and the linear parts of the correction terms. The evolution of cosmological matter structures is shown to be governed by an effective time dependent Newton's constant. We also analyze the propagation of the perturbation modes. Tensor and vector modes are only slightly modified, but two new scalar degrees of freedom are present. Their causality and stability is demonstrated, and their formal ghost conditions are related to a singularity of the cosmological background. In general, the Newtonian limit of these models has no apparent conflicts with observations but can provide useful constraints.