Evidence for and Obstructions to Non-Linear Partially Massless Gravity
Claudia de Rham, Kurt Hinterbichler, Rachel A. Rosen, Andrew J. Tolley
TL;DR
This work investigates whether a fully non-linear partially massless (PM) gravity theory can exist within ghost-free massive gravity with a de Sitter reference metric. It assembles multiple lines of evidence—decoupling-limit analysis, mini-superspace FRW studies, FRW perturbations, and explicit cubic-order checks—that point to a unique PM candidate with specific coefficient choices. However, the authors uncover obstructions at anisotropic, quartic, and full quartic orders that prevent extending the PM symmetry beyond cubic order in the standard Einstein-Hilbert framework. The result constitutes a no-go: non-linear PM gravity cannot be realized in the investigated setup, though potential avenues (non-canonical kinetic terms, additional fields, or bimetric generalizations) remain worth exploring for connections to the cosmological constant problem.
Abstract
Non-linear partially massless (PM) gravity, if it exists, is a theory of massive gravity in which the graviton has four propagating degrees of freedom. In PM gravity, a scalar gauge symmetry removes one of the five modes of the massive graviton. This symmetry ties the value of the cosmological constant to the mass of the graviton, which in turn can be kept small in a technically natural way. Thus PM gravity could offer a compelling solution to the old cosmological constant problem. In this work we look for such a theory among the known ghost-free massive gravity models with a de Sitter reference metric. We find that despite the existence of strong supporting evidence for the existence of a PM theory of gravity, technical obstructions arise which preclude its formulation using the standard massive gravity framework.