Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion

TL;DR

This paper develops a comprehensive framework for viable modified $f(R)$ gravity models that unify early universe inflation and late-time acceleration, ensuring they pass local tests and are phenomenologically promising.

Contribution

Introduces a class of exponential, step-class $f(R)$ gravity models that naturally unify inflation and acceleration while satisfying all local observational constraints.

Findings

Models naturally unify inflation and late-time acceleration.

Models pass all local tests including stability and Newtonian limits.

Explicit analysis of one- and two-step models, extendable to N-step models.

Abstract

A general approach to viable modified $f(R)$ gravity is developed in both the Jordan and the Einstein frames. A class of exponential, realistic modified gravities is introduced and investigated with care. Special focus is made on step-class models, most promising from the phenomenological viewpoint and which provide a natural way to classify all viable modified gravities. One- and two-steps models are explicitly considered, but the analysis is extensible to $N$-step models. Both inflation in the early universe and the onset of recent accelerated expansion arise in these models in a natural, unified way. Moreover, it is demonstrated that models in this category easily pass all local tests, including stability of spherical body solution, non-violation of Newton's law, and generation of a very heavy positive mass for the additional scalar degree of freedom.