Unification of Constant-roll Inflation and Dark Energy with Logarithmic $R^2$-corrected and Exponential $F(R)$ Gravity

TL;DR

This paper explores a unified $F(R)$ gravity framework to describe both early inflation and late dark energy acceleration, ensuring compatibility with observations and addressing oscillation issues.

Contribution

It introduces specific $F(R)$ models that unify inflation and dark energy, analyzing their viability and observational consistency.

Findings

Achieved viable inflationary models compatible with data

Demonstrated potential to unify early and late acceleration eras

Identified models with minimal dark energy oscillations

Abstract

In this paper we investigate how to describe in a unified way a constant-roll inflationary era with a dark energy era, by using the theoretical framework of $F(R)$ gravity. To this end, we introduce some classes of appropriately chosen $F(R)$ gravity models, and we examine in detail how the unification of early and late-time acceleration eras can be achieved. We study in detail the inflationary era, and as we demonstrate it is possible to achieve a viable inflationary era, for which the spectral index of primordial curvature perturbations and the scalar-to-tensor ratio can be compatible with the latest observational data. In addition, the graceful exit issue is briefly discussed for a class of models. Finally, we discuss the dark energy oscillations issue, and we investigate which model from one of the classes we introduced, can produce oscillations with the smallest amplitude.