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

Understand

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.