New Branches of Massive Gravity
Denis Comelli, Marco Crisostomi, Kazuya Koyama, Luigi Pilo and, Gianmassimo Tasinato

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 , where is the inverse of the physical metric and 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
