Stability of de Sitter Solutions in Non-local Cosmological Models

TL;DR

This paper investigates the stability of de Sitter solutions in a non-local gravity model involving an exponential function of the inverse d'Alembertian of the Ricci scalar, analyzing perturbations in anisotropic cosmologies.

Contribution

It provides a stability analysis of de Sitter solutions in a non-local gravity model with exponential form, without parameter restrictions, using Hubble-normalized variables.

Findings

Derived sufficient conditions for stability of de Sitter solutions.

Analyzed perturbations in Bianchi I metric with zero cosmological constant.

Explored stability criteria applicable to non-local cosmological models.

Abstract

A non-local gravity model, which includes a function $f(\Box^{-1} R)$, where $\Box$ is the d'Alembert operator, is considered. For the model with an exponential $f(\Box^{-1} R)$ de Sitter solutions are explored, without any restrictions on the parameters. Using Hubble-normalized variables, the stability of the de Sitter solutions is investigated, with respect to perturbations in the Bianchi I metric, in the case of zero cosmological constant, and sufficient conditions for stability are obtained.