No consistent bimetric gravity?

TL;DR

The paper investigates whether ghost-free bimetric gravity (BMG) can support a nonlinear partially massless (PM) gauge symmetry. By analyzing the BMG action in a vierbein formalism, deriving the vector constraints and Bianchi identities, and examining linearized fluctuations around diagonal Einstein vacua, the authors identify a linear PM sector at special tunings but argue that no covariant nonlinear PM extension exists. They reason that a covariant scalar constraint and a corresponding PM Bianchi identity do not arise in BMG, in part due to Riemann terms from the second metric that cannot be eliminated. Consequently, a consistent PM BMG is deemed unlikely, suggesting that GR-like isolation persists among two-field gravity theories. The work also discusses potential but challenging directions for modifying or embedding BMG within broader theoretical frameworks to circumvent these obstacles.

Abstract

We discuss the prospects for a consistent, nonlinear, partially massless (PM), gauge symmetry of bimetric gravity (BMG). Just as for single metric massive gravity, we show that consistency of BMG relies on it having a PM extension; we then argue that it cannot.