Torsion/non-metricity duality in f(R) gravity

TL;DR

This paper explores the duality between torsion and nonmetricity in f(R) gravity, showing their physical equivalence and potential roles in cosmological acceleration within affine spacetime geometries.

Contribution

It reveals a duality between torsion and nonmetricity in pure f(R) gravity, demonstrating their equivalence through projective transformations and their potential as sources of cosmic acceleration.

Findings

Torsion and nonmetricity are related by projective transformations in R2 gravity.

Both can act as geometric sources of accelerated expansion.

Torsion and nonmetricity are physically equivalent in the context studied.

Abstract

Torsion and nonmetricity are inherent ingredients in modifications of Eintein's gravity that are based on affine spacetime geometries. In the context of pure f(R) gravity we discuss here, in some detail, the relatively unnoticed duality between torsion and nonmetricity. In particular we show that for R2 gravity torsion and nonmetricity are related by projective transformations. Since the latter correspond simply to redefining the affine parameters of autoparallels, we conclude that torsion and nonmetricity are physically equivalent properties of spacetime. As a simple example we show that both torsion and nonmetricity can act as geometric sources of accelerated expansion in a spatially homogenous cosmological model within R2 gravity and we brie y discuss possible implications of our results.