Oscillations of the F(R) dark energy in the accelerating universe

TL;DR

This paper investigates oscillations of F(R) dark energy around the phantom divide line during different cosmic epochs, analyzing stability and potential singularities with numerical confirmation in exponential gravity models.

Contribution

It provides a detailed analysis of dark energy oscillations in F(R) gravity during matter and de Sitter epochs, including stability, perturbations, and singularity relations, with numerical validation.

Findings

Dark energy oscillates around ω_DE = -1 during cosmic evolution.

Matter epoch is a stable point for high redshift values.

Oscillations are linked to possible singularities in the model.

Abstract

Oscillations of the $F(R)$ dark energy around the phantom divide line, $\omega_{DE}=-1$, both during the matter era and also in the de Sitter epoch are investigated. The analysis during the de Sitter epoch is revisited by expanding the modified equations of motion around the de Sitter solution. Then, during the matter epoch, the time dependence of the dark energy perturbations is discussed by using two different local expansions. For high values of the red shift, the matter epoch is a stable point of the theory, giving the possibility to expand the $F(R)$-functions in terms of the dark energy perturbations. In the late-time matter era, the realistic case is considered where dark energy tends to a constant. The results obtained are confirmed by precise numerical computation on a specific model of exponential gravity. A novel and very detailed discussion is provided on the critical points in the matter era and on the relation of the oscillations with possible singularities.