Searches for beyond-Riemann gravity

Many effective field theories describing gravity cannot arise from an underlying theory based on Riemann geometry or its extensions to include torsion and nonmetricity but may instead emerge another have a nongeometric basis. The Lagrange density for broad class of such is investigated. action fermions coupled linearized about Minkowski background found terms small deviations Lorentz invariance gravitational gauge invariance. corresponding nonrelativistic hamiltonian derived at second order in the fermion momentum. implications laboratory experiments astrophysical observations with are studied, primary focus anomalous spin-gravity couplings. First constraints some coefficients extracted existing data obtained via measurements different potentials, comparisons accelerations, interferometric methods, investigations bound states. Some prospects future experimental studies discussed.