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$R^2$-corrected dark energy (DE) models in $F(R)$ gravity have been widelyinvestigated in recent years, which not only removes the weak singularitypotentially present in DE models but also provide us with a unified picture ofthe cosmic history, including the inflationary and DE epochs. Towards theunified interpretation of dynamical DE all over the cosmic history in the classof $R^2$-corrected DE models, we explore the universal features of the scalarondynamics in the radiation-dominated epoch, along with the chameleon mechanism,by keeping our eyes on the inflationary and DE epochs. We show that thescalaron evolution does not follow a \textit{surfing solution} and is mostlyadiabatic before big bang nucleosynthesis (BBN), even properly including the\textit{kick} by the nonperturbative QCD phase transition, hence a catastrophicconsequence claimed in the literature is not applied to this class of DEmodels. 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-inflationaryepoch would be pretty different from what the standard $R^2$ inflationaryscenario undergoes due to the presence of the chameleon mechanism.

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