f(R) Gravity with Torsion: The Metric-Affine Approach

TL;DR

This paper explores f(R) gravity incorporating torsion within the metric-affine formalism, proposing a geometric scalar field that could explain dark energy and dark matter phenomena in cosmology.

Contribution

It introduces a novel approach to f(R) gravity with torsion, linking extra degrees of freedom to a geometric scalar field and analyzing their cosmological implications.

Findings

Torsion and curvature degrees of freedom can be represented as an effective scalar field.

The geometric scalar field may account for dark energy and dark matter effects.

The formalism extends the Palatini approach to include torsion effects in f(R) gravity.

Abstract

The role of torsion in f(R) gravity is considered in the framework of metric-affine formalism. We discuss the field equations in empty space and in presence of perfect fluid matter taking into account the analogy with the Palatini formalism. As a result, the extra curvature and torsion degrees of freedom can be dealt as an effective scalar field of fully geometric origin. From a cosmological point of view, such a geometric description could account for the whole Dark Side of the Universe.