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

Abstract

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 ${\Lambda }_3$ 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. However, the equation of motion for $\pi$ 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.

16 pages, 1 figure; v2 published version

References in corpus (1)

• Resummation of Massive Gravity

Cited by in corpus (2)

• Gauged Galileons
• On covariant expansion of the gravitational Stückelberg trick