Explicit versus Spontaneous Diffeomorphism Breaking in Gravity

Understand

Gravitational theories with fixed background fields break local Lorentz and diffeomorphism invariance either explicitly or spontaneously.

• In the case of explicit breaking it is known that conflicts can arise between the dynamics and geometrical constraints, while spontaneous breaking evades this problem.
• It is for this reason that in the gravity sector of the Standard-Model Extension (SME) it is assumed that the background fields (SME coefficients) originate from spontaneous symmetry breaking.
• However, in other examples, such as Chern-Simons gravity and massive gravity, diffeomorphism invariance is explicitly broken by the background fields, and the potential conflicts between the dynamics and geometry can be avoided in most cases.