Connecting early and late universe by $f(R)$ gravity

TL;DR

This review explores how $f(R)$ gravity can unify descriptions of the early inflationary universe and the current dark energy-driven acceleration, highlighting its potential as a geometric framework for cosmology.

Contribution

It provides a concise overview of $f(R)$ gravity's role in modeling both early and late universe accelerated phases, emphasizing its fundamental physics motivations and main components.

Findings

$f(R)$ gravity can describe both inflation and dark energy.

The paper summarizes key aspects of $f(R)$ inflation and quintessence.

It outlines the main ingredients of $f(R)$ cosmography.

Abstract

Inflation and dark energy are two of the most relevant aspects of modern cosmology. These different epochs provide the universe is passing through accelerated phases soon after the Big-Bang and at present stage of its evolution. In this review paper, we discuss that both eras can be, in principle, described by a geometric picture, under the standard of $f(R)$ gravity. We give the fundamental physics motivations and outline the main ingredients of $f(R)$ inflation, quintessence and cosmography. This wants to be a quick summary of $f(R)$ paradigm without claiming of completeness.