Gravity with Explicit Diffeomorphism Breaking

TL;DR

This paper explores theories of gravity that explicitly break diffeomorphism invariance, demonstrating their consistency and analyzing specific models like massive gravity and Hořava gravity, with implications for matter-gravity interactions.

Contribution

It shows how the Standard-Model Extension framework can be applied to explicit diffeomorphism breaking theories, previously thought only suitable for spontaneous breaking.

Findings

Explicit breaking theories can satisfy consistency conditions with matter couplings.

Bounds on matter-gravity interactions with explicit breaking are derived.

Examples include massive gravity and Hořava gravity models.

Abstract

Modified theories of gravity that explicitly break diffeomorphism invariance have been used for over a decade to explore open issues related to quantum gravity, dark energy, and dark matter. At the same time, the Standard-Model Extension (SME) has been widely used as a phenomenological framework in investigations of spacetime symmetry breaking. Until recently, it was thought that the SME was suitable only for theories with spontaneous spacetime symmetry breaking due to consistency conditions stemming from the Bianchi identities. However, it has recently been shown that, particularly with matter couplings included, the consistency conditions can also be satisfied in theories with explicit breaking. An overview of how this is achieved is presented, and two examples are examined. The first is massive gravity, which includes a nondynamical background tensor. The second is a model based on a low-energy limit of Ho\v rava gravity, where spacetime has a physically preferred foliation. In both cases, bounds on matter--gravity interactions that explicitly break diffeomorphisms are obtained using the SME.