Searches for beyond-Riemann gravity

TL;DR

This paper explores theories of gravity that extend beyond traditional Riemannian geometry, analyzing their implications for fermions, Lorentz invariance, and potential experimental tests in laboratory and astrophysical settings.

Contribution

It investigates a broad class of non-Riemannian gravity theories, deriving fermion couplings, Lorentz-violating terms, and initial experimental constraints on these models.

Findings

Derived nonrelativistic Hamiltonian with Lorentz-violating terms

Identified experimental bounds on deviations from standard gravity

Discussed future experimental prospects for testing these theories

Abstract

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 from another geometry or may have a nongeometric basis. The Lagrange density for a broad class of such theories is investigated. The action for fermions coupled to gravity is linearized about a Minkowski background and is found to include terms describing small deviations from Lorentz invariance and gravitational gauge invariance. The corresponding nonrelativistic hamiltonian is derived at second order in the fermion momentum. The implications for laboratory experiments and astrophysical observations with fermions are studied, with primary focus on anomalous spin-gravity couplings. First constraints on some coefficients are extracted from existing data obtained via measurements at different potentials, comparisons of gravitational accelerations, interferometric methods, and investigations of gravitational bound states. Some prospects for future experimental studies are discussed.