Metric-affine $f(R)$-gravity with torsion: an overview

TL;DR

This paper reviews metric-affine f(R)-gravity with torsion, highlighting its potential to explain dark energy and dark matter through geometric degrees of freedom and discussing the associated field equations and initial value problem.

Contribution

It provides an overview of the field equations and the role of torsion and curvature in f(R)-gravity, emphasizing the geometric origin of effective scalar fields.

Findings

Extra curvature and torsion can be represented as an effective scalar field.

The formalism can describe dark energy and dark matter phenomena.

Initial value problem for these theories is addressed.

Abstract

Torsion and curvature could play a fundamental role in explaining cosmological dynamics. f(R)-gravity with torsion is an approach aimed to encompass in a comprehensive scheme all the Dark Side of the Universe (Dark Energy and Dark Matter). We discuss the field equations in empty space and in presence of perfect fluid matter taking into account the analogy with the metric-affine formalism. The result is that the extra curvature and torsion degrees of freedom can be dealt under the standard of an effective scalar field of fully geometric origin. The initial value problem for such theories is also discussed.