Towards a unified interpretation of the early Universe in $R^2$-corrected dark energy model of $F(R)$ gravity

TL;DR

This paper investigates the scalaron dynamics in $R^2$-corrected dark energy models within $F(R)$ gravity, demonstrating their stability before BBN and discussing implications for cosmic inflation and dark energy evolution.

Contribution

It provides a universal analysis of scalaron behavior in $R^2$-corrected $F(R)$ models, addressing stability issues and the impact of the chameleon mechanism across cosmic epochs.

Findings

Scalaron evolution is mostly adiabatic before BBN.

The model avoids catastrophic surfing solutions.

The presence of the chameleon mechanism alters post-inflationary dynamics.

Abstract

$R^2$-corrected dark energy (DE) models in $F(R)$ gravity have been widely investigated in recent years, which not only removes the weak singularity potentially present in DE models but also provide us with a unified picture of the cosmic history, including the inflationary and DE epochs. Towards the unified interpretation of dynamical DE all over the cosmic history in the class of $R^2$-corrected DE models, we explore the universal features of the scalaron dynamics in the radiation-dominated epoch, along with the chameleon mechanism, by keeping our eyes on the inflationary and DE epochs. We show that the scalaron evolution does not follow a \textit{surfing solution} and is mostly adiabatic before big bang nucleosynthesis (BBN), even properly including the \textit{kick} by the nonperturbative QCD phase transition, hence a catastrophic consequence claimed in the literature is not applied to this class of DE models. This is due to the presence of the gigantic scale hierarchy between $R^2$ correction and DE, so is the universal feature for the class of $R^2$-corrected DE models. The prospects for the post- or onset-inflationary epoch would be pretty different from what the standard $R^2$ inflationary scenario undergoes due to the presence of the chameleon mechanism.