A modified model of non-locally corrected gravity: Cosmology and the Newtonian limit

TL;DR

This paper explores a modified non-local gravity model, analyzing its cosmological solutions, stability, and Solar system constraints, revealing conditions for de Sitter solutions and the impact of potential functions on perturbations.

Contribution

It introduces a locally representable non-local gravity model with scalar fields, analyzing its cosmological stability and Solar system constraints, which is a novel approach.

Findings

Existence of stable de Sitter solutions with suitable potentials.

Early universe behavior as a radiation-dominated repeller.

Solar system tests strongly constrain the potential function form.

Abstract

A modified form of non-locally corrected theory of gravity is investigated in the context of cosmology and the Newtonian limit. This form of non-local correction to classic Einstein-Hilbert action can be locally represented by a triple-scalar-tensor theory in which one of the scalar degree of freedom is phantom-like and the other two are quintessence-like. We show that there exists a stable de Sitter solution for the cosmological dynamics if a suitable form of potential function $V(\phi)$ (or equivalently, $f(R)$) is selected. However, no matter what a potential function is selected, there is always an early time repeller solution corresponding to a radiation dominated universe. Besides, the equations for linear scalar perturbations are presented and it is shown that the form of potential function $V(\phi)$ is stringently constrained by the Solar system test, although the post-Newtonian parameter $\gamma$ is not directly affected by this function.