Gravity with background fields and diffeomorphism breaking

TL;DR

This paper discusses effective gravitational theories with background fields that break symmetries, highlighting differences between explicit and spontaneous symmetry breaking and their impact on the theories' properties.

Contribution

It clarifies how explicit versus spontaneous symmetry breaking affects the physical behavior and properties of gravitational theories with background fields.

Findings

Explicit breaking leads to fixed, nondynamical background fields.

Spontaneous breaking involves dynamical background fields, preserving many features of GR.

The nature of symmetry breaking influences the physical consistency of the theories.

Abstract

Effective gravitational field theories with background fields break local Lorentz symmetry and diffeomorphism invariance. Examples include Chern-Simons gravity, massive gravity, and the Standard-Model Extension (SME). The physical properties and behavior of these theories depend greatly on whether the spacetime symmetry breaking is explicit or spontaneous. With explicit breaking, the background fields are fixed and nondynamical, and the resulting theories are fundamentally different from Einstein's General Relativity (GR). However, when the symmetry breaking is spontaneous, the background fields are dynamical in origin, and many of the usual features of Einstein's GR still apply.