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Covariant Stückelberg analysis of de Rham-Gabadadze-Tolley massive gravity with a general fiducial metric

The Stückelberg analysis of nonlinear massive gravity in the presence of a general fiducial metric is investigated. We develop a "covariant" formalism for the Stückelberg expansion by working with a local inertial frame, through which helicity modes can be characterized correctly. Within this covariant approach, an extended $Λ_3$ decoupling limit analysis can be consistently performed, which keeps $\bar{R}_{μνρσ}/m^2$ fixed with $\bar{R}_{μνρσ}$ the Riemann tensor of the fiducial metric. In this extended decoupling limit, the scalar mode $π$ acquires self-interactions due to the presence of the curvature of the fiducial metric. However, the equation of motion for $π$ remains of second order in derivatives, which extends the understanding of the absence of the Boulware Deser ghost in the case of a flat fiducial metric.