Spacetime Nonmetricity and Lorentz Violation

Abstract

Nonmetricity exists in gravitational theories when the connection is not metric compatible. To constrain it experimentally we construct general couplings between nonmetricity and a Dirac fermion in effective field theory. With the assumption of a nonzero background nonmetricity, the theory resembles the fermion sector of the Standard-Model Extension. By carefully choosing experiments that test Lorentz symmetry, their constraints on Lorentz violation are translated to the first experimental bounds on nonmetricity.