Torsion/nonmetricity duality in f(R) gravity

@article{Iosifidis2019TorsionnonmetricityDI,
  title={Torsion/nonmetricity duality in f(R) gravity},
  author={Damianos Iosifidis and Anastasios C. Petkou and Christos G. Tsagas},
  journal={General Relativity and Gravitation},
  year={2019},
  volume={51},
  pages={1-15}
}
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. Our novel suggestion is that torsion and nonmetricity are physically equivalent properties of spacetimes having nontrivial Weyl structure. Our main example is $$R^2$$R2 gravity where torsion and nonmetricity are related by… 
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