Lorentz-violating massive gauge and gravitational fields

TL;DR

The paper investigates nonlinear dynamics of Lorentz-violating massive gauge and gravitational fields, focusing on overcoming the Boulware-Deser instability that plagues many massive gravity theories. It analyzes a LV photon model to illustrate how a theory can have only two massive propagating degrees of freedom yet exhibit long-range instantaneous interactions, motivating the search for BD-stable LV constructions. The authors identify BD-free LV models (two-DOF and multi-DOF variants) that avoid vDVZ discontinuity but retain instantaneous interactions, and they discuss further extensions that alter the DOF count and raise questions about quantum stability. The work highlights a nuanced landscape where BD stability and causality-like features coexist, with potential phenomenological implications depending on the graviton/photon mass scale.

Abstract

We study nonlinear dynamics in models of Lorentz-violating massive gravity. The Boulware-Deser instability restricts severely the class of acceptable theories. We identify a model that is stable. It exhibits the following bizarre but interesting property: there are only two massive propagating degrees of freedom in the spectrum, and yet long-range instantaneous interactions are present in the theory. We discuss this property on a simpler example of a photon with a Lorentz-violating mass term where the issues of (a)causality are easier to understand. Depending on the values of the mass parameter these models can either be excluded, or become phenomenologically interesting. We discuss a similar example with more degrees of freedom, as well as a model without the long-range instantaneous interactions.