Unification of the inflation with late-time acceleration in Born-Infeld-$f(R)$ gravity

TL;DR

This paper demonstrates that Born-Infeld-$f(R)$ gravity can unify early inflation and late-time cosmic acceleration, allowing for complex evolution including phantom-divide crossing, without matter content.

Contribution

It applies a conformal approach to show that Born-Infeld-$f(R)$ gravity can model a realistic universe unifying inflation and dark energy.

Findings

The model can produce periodic and non-periodic cosmic evolution.

It allows crossing the phantom-divide at different cosmic epochs.

The approach extends previous work to include late-time acceleration.

Abstract

We study accelerating dynamics from Born-Infeld-$f(R)$ gravity in a simplified conformal approach without matter. In our work (A.N. Makarenko, S. Odintsov, G.J. Olmo, Phys.Lett. B734 (2014) 36, [arXiv:1403.2850]) it was derived eventually any Dark Energy cosmology from above theory. In this Letter we apply the technique of (arXiv:1403.2850) to show that Born-Infeld-$f(R)$ gravity may describe very realistic universe admitting the unification of early-time inflation with late-time acceleration. Specifically, the evolution with periodic as well as non-periodic behavior is considered with possibility to cross the phantom-divide at early or late-times.