Cosmological perturbations in Massive Gravity and the Higuchi bound

TL;DR

This work analyzes cosmological perturbations in ghost-free massive gravity (dRGT) with an FRW reference metric to generalize the Higuchi bound beyond de Sitter. Using a Hamiltonian approach, the authors derive the second-order scalar-sector action and extract an effective mass tilde{m}^2(H) whose bound tilts against the Vainshtein mechanism. They show that, for FRW-on-FRW backgrounds, the resulting Higuchi-Vainshtein tension strongly constrains the graviton mass parameter and persists across matter equations of state, challenging compatibility with GR-like behavior. The results hold for both dS on dS and FRW-on-FRW scenarios, with Appendix A,B supplying the explicit perturbative coefficients and matrices involved in the stability analysis. The study suggests that resolving the tension may require moving beyond single-metric FRW constructions, potentially pointing toward multi-metric frameworks.

Abstract

In de Sitter spacetime there exists an absolute minimum for the mass of a spin-2 field set by the Higuchi bound m^2 \geq 2H^2. We generalize this bound to arbitrary spatially flat FRW geometries in the context of the recently proposed ghost-free models of Massive Gravity with an FRW reference metric, by performing a Hamiltonian analysis for cosmological perturbations. We find that the bound generically indicates that spatially flat FRW solutions in FRW massive gravity, which exhibit a Vainshtein mechanism in the background as required by consistency with observations, imply that the helicity zero mode is a ghost. In contradistinction to previous works, the tension between the Higuchi bound and the Vainshtein mechanism is equally strong regardless of the equation of state for matter.