The metric-affine formalism of f(R) gravity

TL;DR

This paper explores the metric-affine formalism of f(R) gravity, emphasizing its enriched phenomenology over General Relativity, relevant to both cosmological and small-scale physics.

Contribution

It presents a comprehensive formalism for metric-affine f(R) gravity, highlighting its novel phenomenological features beyond standard GR.

Findings

Enriched phenomenology compared to General Relativity.

Relevance to both cosmological and small-scale physics.

Formalism incorporating independent metric and connection variations.

Abstract

Recently a class of alternative theories of gravity which goes under the name f(R) gravity, has received considerable attention, mainly due to its interesting applications in cosmology. However, the phenomenology of such theories is not only relevant to cosmological scales, especially when it is treated within the framework of the so called Palatini variation, an independent variation with respect to the metric and the connection, which is not considered a priori to be the Levi-Civita connection of the metric. If this connection has its standard geometrical meaning the resulting theory will be a metric-affine theory of gravity, as will be discussed in this talk. The general formalism will be presented and several aspects of the theory will be covered, mainly focusing on the enriched phenomenology that such theories exhibit with respect to General Relativity, relevant not only to large scales (cosmology) but also to small scales (e.g. torsion).