Cosmic history of viable exponential gravity: Equation of state oscillations and growth index from inflation to dark energy era

TL;DR

This paper investigates the behavior of exponential $F(R)$ gravity models, focusing on dark energy oscillations, their stabilization, and applications to inflation, demonstrating a unified description of early and late universe acceleration.

Contribution

It introduces a correction to stabilize dark energy oscillations in exponential gravity models and explores their role in inflation and dark energy evolution.

Findings

Dark energy oscillations can cause singularities at high redshift.

Adding a correction term stabilizes these oscillations without losing viability.

Exponential gravity models can unify inflation and dark energy eras.

Abstract

A generic feature of viable $F(R)$ gravity is investigated: It is demonstrated that during the matter dominated era the large frequency oscillations of the effective dark energy may influence the behavior of higher derivatives of the Hubble parameter with the risk to produce some singular unphysical solutions at high redshift. This behavior is explicitly analyzed for realistic $F(R)$ models, in particular, exponential gravity and a power form model. To stabilize such oscillations, we consider the additional modification of the models via a correction term which does not destroy the viability properties. A detailed analysis on the future evolution of the universe and the evolution history of the growth index of the matter density perturbations are performed. Furthermore, we explore two applications of exponential gravity to the inflationary scenario. We show how it is possible to obtain different numbers of $e$-folds during the early-time acceleration by making different choices of the model parameters in the presence of ultrarelativistic matter, which destabilizes inflation and eventually leads to the exit from the inflationary stage. We execute the numerical analysis of inflation in two viable exponential gravity models. It is proved that at the end of the inflation, the effective energy density and curvature of the universe decrease and thus a unified description between inflation and the $\Lambda$CDM-like dark energy dominated era can be realized.