f(R) gravity with torsion: a geometric approach within the J-bundles framework

TL;DR

This paper explores f(R) gravity theories with torsion using jet-bundles, providing a geometric framework that simplifies the analysis of symmetries, conservation laws, and cosmological applications.

Contribution

It introduces a jet-bundles approach to f(R)-gravity with torsion, enabling a systematic study of field equations, matter interactions, and cosmological implications.

Findings

Field equations derived in vacuum and matter-filled scenarios.

Unified geometric framework for torsion and curvature tensors.

Connections established between f(R)-gravity and scalar-tensor theories.

Abstract

We discuss the f(R)-theories of gravity with torsion in the framework of jet-bundles. Such an approach is particularly useful since the components of the torsion and curvature tensors can be chosen as fiber jet-coordinates on the bundles and then the symmetries and the conservation laws of the theory can be easily achieved. Field equations of f(R)-gravity are studied in empty space and in presence of various forms of matter as Dirac fields, Yang--Mills fields and spin perfect fluid. Such fields enlarge the jet-bundles framework and characterize the dynamics. Finally we give some cosmological applications and discuss the relations between f(R)-gravity and scalar-tensor theories.