Maxwell extension of $f(R)$ gravity

TL;DR

This paper develops a Maxwell extension of $f(R)$ gravity, introducing a cosmological constant and torsion via Maxwell symmetry, and explores the resulting modified gravitational equations and their implications.

Contribution

It constructs a Maxwell-extended $f(R)$ gravity model incorporating a cosmological constant and torsion, which is a novel generalization of existing theories.

Findings

Maxwell symmetry allows geometric cosmological constant in $f(R)$ gravity.

The theory includes a non-zero torsion sourced by an antisymmetric gauge field.

New terms in gravitational equations include an energy-momentum tensor for the background field.

Abstract

Inspired by the Maxwell symmetry generalization of general relativity (Maxwell gravity), we have constructed the Maxwell extension of $f(R)$ gravity. We found that the semi-simple extension of the Poincare symmetry allows us to introduce geometrically a cosmological constant term in four-dimensional $f(R)$ gravity. This symmetry also allows the introduction of a non-vanishing torsion to the Maxwell $f(R)$ theory. It is found that the antisymmetric gauge field $B^{ab}$ associated with Maxwell extension is considered as a source of the torsion. It is also found that the gravitational equation of motion acquires a new term in the form of an energy-momentum tensor for the background field. The importance of these new equations is briefly discussed.