A bird's eye view of f(R)-gravity

TL;DR

This paper surveys various formulations of $f(R)$ gravity theories, exploring their applications to cosmic acceleration, gravitational waves, and discussing their successes and challenges in meeting viability criteria.

Contribution

It provides a comprehensive overview of $f(R)$ gravity theories, including their formulations, applications, and the theoretical and experimental challenges they face.

Findings

$f(R)$ theories can model cosmic acceleration without dark energy.

They face theoretical and experimental viability challenges.

Theories have successes in explaining certain gravitational phenomena.

Abstract

We survey the landscape of $f(R)$ theories of gravity in their various formulations, which have been used to model the cosmic acceleration as alternatives to dark energy and dark matter. Besides, we take into account the problem of gravitational waves in such theories. We discuss some successes of $f(R)$-gravity (where $f(R)$ is a generic function of Ricci scalar $R$), theoretical and experimental challenges that they face in order to satisfy minimal criteria for viability.