Metric-affine f(R) theories of gravity

TL;DR

This paper explores metric-affine f(R) gravity theories, examining their relation to General Relativity, the role of torsion, and the impact of matter coupling, expanding beyond cosmological applications.

Contribution

It provides a comprehensive analysis of metric-affine f(R) theories, addressing open issues like torsion, matter coupling, and their relation to standard gravity.

Findings

Clarifies the relation between metric-affine f(R) gravity and General Relativity.

Analyzes the effects of matter action dependence on connections.

Investigates the origin and significance of torsion in these theories.

Abstract

General Relativity assumes that spacetime is fully described by the metric alone. An alternative is the so called Palatini formalism where the metric and the connections are taken as independent quantities. The metric-affine theory of gravity has attracted considerable attention recently, since it was shown that within this framework some cosmological models, based on some generalized gravitational actions, can account for the current accelerated expansion of the universe. However we think that metric-affine gravity deserves much more attention than that related to cosmological applications and so we consider here metric-affine gravity theories in which the gravitational action is a general function of the scalar curvature while the matter action is allowed to depend also on the connection which is not {\em a priori} symmetric. This general treatment will allow us to address several open issues such as: the relation between metric-affine $f(R)$ gravity and General Relativity (in vacuum as well as in the presence of matter), the implications of the dependence (or independence) of the matter action on the connections, the origin and role of torsion and the viability of the minimal-coupling principle.