Covariant St\"uckelberg analysis of de Rham-Gabadadze-Tolley massive gravity with a general fiducial metric

Understand

The St\"uckelberg analysis of nonlinear massive gravity in the presence of a general fiducial metric is investigated.

• We develop a "covariant" formalism for the St\"uckelberg expansion by working with a local inertial frame, through which helicity modes can be characterized correctly.
• Within this covariant approach, an extended $\Lambda_3$ decoupling limit analysis can be consistently performed, which keeps $\bar{R}_{\mu\nu\rho\sigma}/m^2$ fixed with $\bar{R}_{\mu\nu\rho\sigma}$ the Riemann tensor of the fiducial metric.
• In this extended decoupling limit, the scalar mode $\pi$ acquires self-interactions due to the presence of the curvature of the fiducial metric.