Resolving the Ghost Problem in non-Linear Massive Gravity

Abstract

We analyze the ghost issue in the recently proposed models of non-linear massive gravity in the ADM formalism. We show that, in the entire two-parameter family of actions, the Hamiltonian constraint is maintained at the complete non-linear level and we argue for the existence of a non-trivial secondary constraint. This implies the absence of the pathological Boulware-Deser ghost to all orders. To our knowledge, this is the first demonstration of the existence of a consistent theory of massive gravity at the complete non-linear level, in four dimensions.

4 pages, comments and reference added, version accepted for publication

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• Resummation of Massive Gravity
• On Non-Linear Actions for Massive Gravity
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• Topological dyonic black holes of massive gravity with generalized quasitopological electromagnetism
• Derivative couplings in massive bigravity
• Primordial Gravitational Waves in Bimetric Gravity
• Non-minimal Energy-momentum squared gravity
• Translation invariant time-dependent solutions to massive gravity
• Vacua and instantons of ghost-free massive gravity
• Massive "spin-2" theories in arbitrary $D\ge 3$ dimensions
• On massive gravity and bigravity in three dimensions
• On the absence of ghosts in quadratic bigravity
• Superluminal Vector in Ghost-free Massive Gravity
• Translation invariant time-dependent solutions to massive gravity II
• A note on the nonuniqueness of the massive Fierz-Pauli theory and spectator fields
• Black Hole Mechanics for Massive Gravitons
• Hamiltonian structure of bi-gravity, problem of ghost and bifurcation
• On the Curvature Invariants of the Massive Banados-Teitelboim-Zanelli Black Holes and Their Holographic Pictures
• Vainshtein Solutions Without Superluminal Modes
• Nonuniqueness of the Fierz-Pauli mass term for a nonsymmetic tensor
• Bose-Einstein condensation as an alternative to inflation
• On the absence of the Boulware-Deser ghost in novel graviton kinetic terms
• Cosmological constant constraints from observation-derived energy condition bounds and their application to bimetric massive gravity
• Relativistic stars in mass-varying massive gravity
• Entropy spectrum of charged BTZ black holes in massive gravity's rainbow
• Gravity with antisymmetric components
• A unifying framework for ghost-free Lorentz-invariant Lagrangian field theories
• Spectral interaction between universes
• Static spheres and Aschenbach effect for black holes in massive gravity
• Dynamical diffeomorphisms
• Constraint on ghost-free bigravity from gravitational Cherenkov radiation
• Cosmological Study in Myrzakulov $F(R,T)$ Quasi-dilaton Massive Gravity
• Gravitational wave oscillations in bimetric cosmology
• Boulware-Deser ghost in extended quasidilaton massive gravity
• Cosmological future singularities in massive gravity and massive bigravity
• GUP corrected entropy of the Schwarzschild black hole in holographic massive gravity
• Stability analysis for new theories of massive spin-two particle and black hole entropy of new bigravity
• Massive spin-2 theories
• Towards a sound massive cosmology
• Hamiltonian Analysis of Minimal Massive Gravity Coupled to Galileon Tadpole Term
• Gravitational-wave energy and other fluxes in ghost-free bigravity
• Complexity growth of BTZ black hole in massive gravity with a null string
• Perturbations of Cosmological and Black Hole Solutions in Massive gravity and Bi-gravity
• Dark Energy and Inflation with Volume Normalized Action
• Dark energy as an elastic strain fluid
• Pole-skipping for massive fields and the Stueckelberg formalism
• Holographic Aspects of a Higher Curvature Massive Gravity
• Dealing with ghost-free massive gravity without explicit square roots of matrices
• Massive graviton on arbitrary background: derivation, syzygies, applications
• New measures to test modified gravity cosmologies
• Structure of $3D$ gravastars in the context of massive gravity
• Cosmological evolutions of $F(R)$ nonlinear massive gravity
• Dark Energy and Doubly Coupled Bigravity
• Dark Matter phenomenology : from simplified WIMP models to refined alternative solutions
• dRGT theory of massive gravity from spontaneous symmetry breaking
• Axionic extension of the Proca action
• Primordial fluctuations from inflation in dRGT bimetric theory of gravity
• Linear growth of structure in projected massive gravity
• Scalar Field in Massive BTZ Black Hole and Entanglement Entropy
• Nonholonomic Jet Deformations and Exact Solutions for Modified Ricci Soliton and Einstein Equations
• On strong coupling scales in (minimal) massive gravity
• On the ghost issue of extended quasidilaton
• Cosmology and stability in scalar tensor bigravity with non-minimal kinetic coupling gravity
• Mass spectrum and linear perturbations of ghost-free multi-spin-2 theory
• Massive strings from a haunted field theory
• Constant Curvature Solutions of Minimal Massive Gravity
• Bi-Connected Gauss-Bonnet Gravity
• Unusual square roots in the ghost-free theory of massive gravity
• The equivalence between Finsler and non-commutative geometries by massive gravity black hole
• SO(4; 2) and derivatively coupled dRGT massive gravity
• Spherical gravitational waves and quasi-spherical waves scattered from black string in massive gravity
• Modelling gravity on a hyper-cubic lattice
• Constraint Algebra in Bigravity
• Nonlocal Galileons and Self-Acceleration
• On scale-free extensions of massive (bi-)gravity
• Symplectic realization of two interacting spin-two fields in three dimensions
• Towards construction of ghost-free higher derivative gravity from bigravity
• Constrained dynamics of two interacting relativistic particles in the Faddeev-Jackiw symplectic framework
• Thermal X-ray signatures in late-stage unequal-mass massive black hole binary mergers
• Dynamically induced spin-2 mass in a Weyl-invariant framework
• Beyond dRGT - a new massive gravity theory?
• Note About Consistent Extension of Quasidilaton Massive Gravity
• Coexistence curve and molecule number density of AdS topological charged black hole in massive gravity
• Effective Matter Cosmologies of Massive Gravity: Physical Fluids
• de Sitter Branes in a Flat Bulk of Massive Gravity
• Massive spin-2 particles via embedment of the Fierz-Pauli equations of motion
• Tighter bounds on a hypothetical graviton screening mass from the gravitational wave observation GW150914 at LIGO
• Black Holes in Multi-Metric Gravity II: Hairy Solutions and Linear Stability of the Non- and Partially Proportional Branches
• On five-dimensional massive (bi-)gravity
• Generalized interaction in multigravity
• 5-Dimensional Chern-Simons Gauge Theory on an Interval: Massive Spin-2 Theory from Symmetry Breaking via Boundary Conditions
• The Cosmological Impact of Brane-Chern-Simons Massive Gravity
• Power counting renormalizability of quantum gravity in Lifshitz spacetime
• New cosmological solutions in massive gravity theory
• Gauss-Bonnet modification to Hawking evaporation of AdS black holes in massive gravity
• Cosmology of Quasi-Dilaton Massive Gravity with Non-minimal Kinetic Coupling
• Doubly coupled matter fields in massive bigravity
• Bigravity from gradient expansion
• Observational constraints on massive gravity
• Translation invariant time-dependent massive gravity: Hamiltonian analysis
• Fundamental fields around compact objects: Massive spin-2 fields, Superradiant instabilities and Stars with dark matter cores
• A braneworld model in a massive gravity
• A note on higher rank descriptions of massless and massive spin-1 particles
• Gravitational wave propagation in bigravity in the late universe
• Cosmology in warped massive gravity
• Oscillating universe in massive bigravity
• A link between ghost-free bimetric and Eddington-inspired Born-Infeld theory
• Thermodynamics and phase transitions of charged-AdS black holes in dRGT massive gravity with nonlinear electrodynamics
• Note on Covariant Stückelberg Formalism and Absence of Boulware-Deser Ghost in Bi-gravity
• Gauge generator for bi-gravity and multi-gravity models
• Nonlinear interactions for massive spin-2 fields
• Tuning the Cosmological Constant, Broken Scale Invariance, Unitarity
• Static Scalar Field Solutions in Symmetric Gravity
• BB mode angular power spectrum of CMB from massive gravity
• Hamiltonian analysis and positivity of a new massive spin-2 model
• Multiple-scale analysis of modified gravitational-wave propagation
• Ghost-free higher order gravity from bi-gravity
• Large-$N$ Random Matrix Gravity and the Double Hierarchy Problem
• New effective theories of gravitation and their phenomenological consequences
• Supergravity Induced Interactions on Thick Branes
• New model of massive spin two field
• Complexity of the Einstein-Born-Infeld-Massive Black holes
• Topological charge and black hole photon spheres in massive gravity
• Covariant constraints of massive gravity in metric formulation
• Polarized solitons in higher-spin wave dark matter
• On two-vierbein gravity action from gauge theory of conformal group
• Massive Gravity: A Lorentz-Symmetric Aether
• Quantum Phase Space Description of a Cosmological Minimal Massive Bigravity Model
• Self-interacting charged massive spin two particles in Minkowski spacetime
• Multigravity and the cosmological constant
• Generalized Vaidya solutions in bimetric gravity
• GEMS embeddings of Hayward regular black holes in massless and massive gravities
• Effective Fluid FLRW Cosmologies of Minimal Massive Gravity
• Cosmological Solution Moduli of Bigravity
• A note on the uniqueness of the dRGT massive gravity theory
• Relativistic star solutions in Mass-varying Massive Gravity with a diagonal metric
• Canonical formalism of bigravity
• Dipolar perturbations of nonbidiagonal black holes in bigravity
• Algebraic aspects of massive gravity
• Higher-Dimensional Minimal Theory of Mass-Varying Massive Gravity And Its Cosmological Consequences
• The Canonical Structure of Bigravity
• Decoupling Solution Moduli of Bigravity
• Measuring the speed of scalar induced gravitational waves from observations
• Bimetric interactions based on metric congruences
• Weak field limit in vierbein-Einstein-Palatini formalism and Fierz-Pauli Equation