Modifying the theory of gravity by changing independent variables

Abstract

We study some particular modifications of gravity in search for a natural way to unify the gravitational and electromagnetic interaction. The certain components of connection in the appearing variants of the theory can be identified with electromagnetic potential. The methods of adding matter in the form of scalar and spinor fields are studied. In particular, the expansion of the local symmetry group up to GL(2, C) is explored, in which equations of Einstein, Maxwell and Dirac are reproduced for the theory with Weyl spinor.⋆

Emergent Planck mass and dark energy from affine gravity

“…This possibility is, at present, speculative yet rather intriguing. In particular, this observation might be relevant for attempts to unify electromagnetism with gravity both in affine [8,18,21,24,48] and standard approaches [47,49,50]. We would also like to make contact with the idea that gravity should be described by a spin-2 field with spin-2 gauge invariance or general covariance [51][52][53][54][55].…”