New Branches of Massive Gravity

TL;DR

This paper explores different branches of massive gravity theories, showing that only the de Rham-Gabadadze-Tolley potential is well-defined around Minkowski space, but alternative potentials exist when Lorentz symmetry is broken spontaneously.

Contribution

The paper identifies the unique perturbatively well-defined branch of massive gravity around Minkowski space and constructs new Lorentz-invariant, ghost-free potentials breaking Lorentz boosts.

Findings

Only the dRGT potential is perturbatively well-defined around Minkowski.

New ghost-free potentials are constructed with spontaneous Lorentz symmetry breaking.

Alternative branches exist when Lorentz symmetry is broken spontaneously.

Abstract

The basic building block for Lorentz invariant and ghost free massive gravity is the square root of the combination $g^{-1}\eta\,$, where $g^{-1}$ is the inverse of the physical metric and $\eta$ is a reference metric. Since the square root of a matrix is not uniquely defined, it is possible to have physically inequivalent potentials corresponding to different branches. We show that around Minkowski background the only perturbatively well defined branch is the potential proposed by de Rham, Gabadadze and Tolley. On the other hand, if Lorentz symmetry is broken spontaneously, other potentials exist with a standard perturbative expansion. We show this explicitly building new Lorentz invariant, ghost-free massive gravity potentials for theories that in the background preserve rotational invariance, but break Lorentz boosts.