On Partially Massless Bimetric Gravity

TL;DR

This paper extends the Higuchi bound and partial masslessness from linear theories to ghost-free nonlinear bimetric gravity by analyzing linear PM transformations on de Sitter backgrounds and enforcing their compatibility with dynamical backgrounds. By working with a dynamically determined background and the bimetric interaction potential, the authors derive a necessary condition for a nonlinear PM symmetry, which fixes all but one of the β_n parameters and identifies a unique candidate theory. They show that a nonlinear scaling symmetry can integrate the linear PM transformations, yielding a nonlinear PM candidate in four dimensions, though a full proof of the PM symmetry remains unresolved. The work clarifies the relationship between PM behavior and background dynamics and discusses extensions to higher dimensions, decoupling limits, and the massive gravity limit, as well as ongoing debates in the field.

Abstract

We extend the notion of the Higuchi bound and partial masslessness to ghost-free nonlinear bimetric theories. This can be achieved in a simple way by first considering linear massive spin-2 perturbations around maximally symmetric background solutions, for which the linear gauge symmetry at the Higuchi bound is easily identified. Then, requiring consistency between an appropriate subset of these transformations and the dynamical nature of the backgrounds, fixes all but one parameter in the bimetric interaction potential. This specifies the theory up to the value of the Fierz-Pauli mass and leads to the unique candidate for nonlinear partially massless bimetric theory.