Matter-gravity scattering in the presence of spontaneous Lorentz violation

TL;DR

This paper explores how spontaneous Lorentz violation in quantum gravity, modeled via bumblebee fields, affects the gravitational potential, leading to anisotropic corrections and a Darwin-like term.

Contribution

It provides the first calculation of nonrelativistic gravitational potential corrections due to spontaneous Lorentz violation in bumblebee models.

Findings

Anisotropic modifications to Newtonian potential.

Presence of a Darwin-like correction term.

Implications for Lorentz-violating quantum gravity theories.

Abstract

Considering quantum gravity within the framework of effective field theory, we investigated the consequences of spontaneous Lorentz violation for the gravitational potential. In particular, we focus our attention on the bumblebee models, in which the graviton couples to a vector $B_{\mu}$ that assumes a nonzero vacuum expectation value. The leading order corrections for the nonrelativistic potential are obtained from calculation of the scattering matrix of two scalar particles interacting gravitationally. These corrections imply anisotropic properties associated with the bumblebee background and also add a Darwin-like term for Newton's potential.