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.

arXiv comment16 pages, 1 figure; v2 published version

References in corpus (22)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• The galileon as a local modification of gravity
• Resummation of Massive Gravity
• Generalization of the Fierz-Pauli Action
• Resolving the Ghost Problem in non-Linear Massive Gravity
• Effective Field Theory for Massive Gravitons and Gravity in Theory Space
• Confirmation of the Secondary Constraint and Absence of Ghost in Massive Gravity and Bimetric Gravity
• Ghost-free Massive Gravity with a General Reference Metric
• On Non-Linear Actions for Massive Gravity
• Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
• Ghosts in Massive Gravity
• Ghost free Massive Gravity in the Stückelberg language
• Cosmological perturbations of self-accelerating universe in nonlinear massive gravity
• Proof of Consistency of Nonlinear Massive Gravity in the Stuckelberg Formulation
• Cosmological Stability Bound in Massive Gravity and Bigravity
• Ghosts, Strong Coupling and Accidental Symmetries in Massive Gravity
• A Proof Of Ghost Freedom In de Rham-Gabadadze-Tolley Massive Gravity
• Massive Gravity on de Sitter and Unique Candidate for Partially Massless Gravity
• Hidden Gravity in Open-String Field Theory
• Complete Decoupling Limit of Ghost-free Massive Gravity
• Covariant Approach to the No-ghost Theorem in Massive Gravity

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• The decoupling limit of Multi-Gravity: Multi-Galileons, Dualities and More
• Coupling between Galileon and massive gravity with composite metrics
• Shift-Symmetric Spin-1 Theories
• Gauged Galileons
• Metamorphosis of the Cosmological Constant and 5D Origin of the Fiducial Metric
• On covariant expansion of the gravitational Stückelberg trick
• Note on Covariant Stückelberg Formalism and Absence of Boulware-Deser Ghost in Bi-gravity