Cosmological perturbations in Massive Gravity and the Higuchi bound

TL;DR

This paper extends the Higuchi bound to general FRW spacetimes within ghost-free Massive Gravity models, revealing a fundamental tension between stability conditions and the Vainshtein mechanism.

Contribution

It generalizes the Higuchi bound to arbitrary FRW geometries in Massive Gravity and analyzes the resulting ghost conditions for cosmological solutions.

Findings

The helicity zero mode is a ghost in these models.

The tension between the Higuchi bound and the Vainshtein mechanism is independent of matter's equation of state.

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.