Matter-gravity couplings and Lorentz violation

Abstract

The gravitational couplings of matter are studied in the presence of Lorentz and $CPT$ violation. At leading order in the coefficients for Lorentz violation, the relativistic quantum Hamiltonian is derived from the gravitationally coupled minimal standard-model extension. For spin-independent effects, the nonrelativistic quantum Hamiltonian and the classical dynamics for test and source bodies are obtained. A systematic perturbative method is developed to treat small metric and coefficient fluctuations about a Lorentz-violating and Minkowski background. The post-Newtonian metric and the trajectory of a test body freely falling under gravity in the presence of Lorentz violation are established. An illustrative example is presented for a bumblebee model. The general methodology is used to identify observable signals of Lorentz and $CPT$ violation in a variety of gravitational experiments and observations, including gravimeter measurements, laboratory and satellite tests of the weak equivalence principle, antimatter studies, solar-system observations, and investigations of the gravitational properties of light. Numerous sensitivities to coefficients for Lorentz violation can be achieved in existing or near-future experiments at the level of parts in $10^3$ down to parts in $10^{15}$. Certain coefficients are uniquely detectable in gravitational searches and remain unmeasured to date.