Inflation and dark energy from $f(R)$ gravity

TL;DR

This paper explores extended $f(R)$ gravity models to address inflationary issues and identify parameter regions consistent with PLANCK data, suggesting a link between stable Einstein frame minima and dark energy.

Contribution

It introduces extended $f(R)$ models like $R + eta R^n$ and their Brans-Dicke generalizations, analyzing their viability and connection to dark energy.

Findings

Parameter space consistent with PLANCK data identified.

Stable Einstein frame minima with non-zero vacuum energy found.

Extended models can address inflationary issues and dark energy connection.

Abstract

Inflationary paradigm has several issues, such as the pre-inflationary horizon problem or the eternal inflation. To avoid that the standard Starobinsky inflation has been extended to $R + \alpha R^n$ and $R + \alpha R^n -\delta R^{2-n}$ models as well as Brans-Dicke generalisation of those $f(R)$ models. The region of the parameter space, which provides consistency with PLANCK data and lack of eternal inflation has been founded. The Einstein frame potential has a stable minimum with non-zero vacuum energy, which may be a source of dark energy.