  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.
