f(R) and f(T) theories of modified gravity

TL;DR

This paper reviews modified gravity theories, specifically f(R) and f(T) models, discussing their formulations, scalar-tensor representations, cosmological applications, and unresolved issues like extra degrees of freedom.

Contribution

It provides a comparative overview of f(R) and f(T) theories, highlighting their formulations, mechanisms, and cosmological applications, along with open questions.

Findings

f(R) theories can be formulated in metric and Palatini approaches

f(T) theories deform teleparallel gravity for cosmological modeling

Both theories involve additional degrees of freedom, with unresolved issues

Abstract

We briefly review f(R) theories, both in the metric and Palatini formulations, their scalar-tensor representations and the chameleon mechanism that could explain the absence of perceptible consequences in the Solar System. We also review f(T) theories, a different approach to modified gravity consisting in a deformation of the teleparallel equivalent of General Relativity. We show some applications to cosmology and cosmic strings. As f(R)'s, f(T) theories are not exempted from additional degrees of freedom; we also discuss this still open issue.