On Non-Linear Actions for Massive Gravity

Abstract

In this work we present a systematic construction of the potentially ghost-free non-linear massive gravity actions. The most general action can be regarded as a 2-parameter deformation of a minimal massive action. Further extensions vanish in 4 dimensions. The general mass term is constructed in terms of a "deformed" determinant from which this property can clearly be seen. In addition, our formulation identifies non-dynamical terms that appear in previous constructions and which do not contribute to the equations of motion. We elaborate on the formal structure of these theories as well as some of their implications.

v3: 22 pages, minor comments added, version to appear in JHEP

References in corpus (15)

• Resummation of Massive Gravity
• Resolving the Ghost Problem in non-Linear Massive Gravity
• Degravitation of the Cosmological Constant and Graviton Width
• Analytic solutions in non-linear massive gravity
• Cosmic Acceleration and the Helicity-0 Graviton
• Exact Schwarzschild-de Sitter black holes in a family of massive gravity models
• Massive Gravity: Resolving the Puzzles
• Unitarity in the Brout-Englert-Higgs Mechanism for Gravity
• Bigravity and Lorentz-violating Massive Gravity
• Massive Gravity: Exorcising the Ghost
• Massive Gravity in Minkowski Space via Gravitational Higgs Mechanism
• Brane Induced Gravity, its Ghost and the Cosmological Constant Problem
• Self-Protection of Massive Cosmological Gravitons
• Unitarity Check in Gravitational Higgs Mechanism
• Exact Solution to the "Auxiliary Extra Dimension" Model of Massive Gravity

Cited by in corpus (300)

• Beyond the Cosmological Standard Model
• Massive Gravity
• Theoretical Aspects of Massive Gravity
• Bimetric Gravity from Ghost-free Massive Gravity
• Resolving the Ghost Problem in non-Linear Massive Gravity
• Testing General Relativity in Cosmology
• Confirmation of the Secondary Constraint and Absence of Ghost in Massive Gravity and Bimetric Gravity
• Ghost-free Massive Gravity with a General Reference Metric
• An introduction to the Vainshtein mechanism
• A systematic approach to generalisations of General Relativity and their cosmological implications
• Interacting Spin-2 Fields
• Ghost free Massive Gravity in the Stückelberg language
• Thermodynamics of Black Holes in Massive Gravity
• Massive spin-2 fields on black hole spacetimes: Instability of the Schwarzschild and Kerr solutions and bounds on the graviton mass
• Does the Hubble constant tension call for new physics?
• Stellar structure models in modified theories of gravity: lessons and challenges
• Bounce cosmology from $F(R)$ gravity and $F(R)$ bigravity
• Universal Resistivity from Holographic Massive Gravity
• Anisotropic stress as signature of non-standard propagation of gravitational waves
• Cosmological perturbations and structure formation in nonlocal infrared modifications of general relativity
• Strong interactions and exact solutions in non-linear massive gravity
• Non-local gravity and dark energy
• Open FRW universes and self-acceleration from nonlinear massive gravity
• Cosmological Solutions in Bimetric Gravity and their Observational Tests
• van der Waals like behaviour of topological AdS black holes in massive gravity
• Black Hole Based Tests of General Relativity
• Cosmology of the Galileon from Massive Gravity
• Accelerated expansion from ghost-free bigravity: a statistical analysis with improved generality
• On Black Holes in Massive Gravity
• Einstein-Born-Infeld-Massive Gravity: adS-Black Hole Solutions and their Thermodynamical properties
• Bimetric gravity is cosmologically viable
• Recent developments in bimetric theory
• On couplings to matter in massive (bi-)gravity
• Proof of Consistency of Nonlinear Massive Gravity in the Stuckelberg Formulation
• Helicity Decomposition of Ghost-free Massive Gravity
• Stable and unstable cosmological models in bimetric massive gravity
• On Consistent Theories of Massive Spin-2 Fields Coupled to Gravity
• Charged Black Hole Solutions in Gauss-Bonnet-Massive Gravity
• Mass-Varying Massive Gravity
• Thermo-electric transport in gauge/gravity models with momentum dissipation
• Trace-anomaly driven inflation in $f(T)$ gravity and in minimal massive bigravity
• Growth Histories in Bimetric Massive Gravity
• Bimetric gravity doubly coupled to matter: theory and cosmological implications
• A non-local theory of massive gravity
• Evidence for and Obstructions to Non-Linear Partially Massless Gravity
• Viable cosmology in bimetric theory
• The Self-Accelerating Universe with Vectors in Massive Gravity
• Charged black holes in nonlinear 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
• Serendipitous discoveries in nonlocal gravity theory
• On Partially Massless Bimetric Gravity
• Cosmological perturbations in massive bigravity
• On the Hamiltonian analysis of non-linear massive gravity
• Relativistic Stars in dRGT Massive Gravity
• Covariant constraints in ghost free massive gravity
• Non-Linear Massive Gravity with Additional Primary Constraint and Absence of Ghosts
• Massive gravity from bimetric gravity
• Gravitational waves in bigravity cosmology
• No-Go Theorems for Unitary and Interacting Partially Massless Spin-Two Fields
• FRW Cosmological Perturbations in Massive Bigravity
• Restoring General Relativity in massive bi-gravity theory
• Higher Derivative Gravity and Conformal Gravity From Bimetric and Partially Massless Bimetric Theory
• Scientific Potential of DECIGO Pathfinder and Testing GR with Space-Borne Gravitational Wave Interferometers
• Cosmic expansion histories in massive bigravity with symmetric matter coupling
• Complete Decoupling Limit of Ghost-free Massive Gravity
• The nature of spacetime in bigravity: two metrics or none?
• Cosmological dynamics and dark energy from non-local infrared modifications of gravity
• Hawking-Page transition in holographic massive gravity
• Stars and Black Holes in Massive Gravity
• A Covariant Master Theory for Novel Galilean Invariant Models and Massive Gravity
• Particular Solutions in Bimetric Theory and Their Implications
• Linear growth of structure in massive bigravity
• Massive Gravity Theories and limits of Ghost-free Bigravity models
• Consistent perturbations in an imperfect fluid
• Higuchi Ghosts and Gradient Instabilities in Bimetric Gravity
• Thermodynamical Structure of AdS Black Holes in Massive Gravity with Stringy Gauge-Gravity Corrections
• On the cosmology of massive gravity
• Multi-Metric Gravity via Massive Gravity
• Cosmology of bigravity with doubly coupled matter
• When is Multimetric Gravity Ghost-free?
• Inhomogeneity simplified
• Note About Hamiltonian Structure of Non-Linear Massive Gravity
• Cosmological perturbations in massive gravity with doubly coupled matter
• Massive cosmological scalar perturbations
• Quantum corrections in massive bigravity and new effective composite metrics
• Gravitational Wave Oscillations in Bigravity
• Classical and quantum massive cosmology for the open FRW universe
• On the local structure of spacetime in ghost-free bimetric theory and massive gravity
• Phase transition of charged black holes in massive gravity through new methods
• On Butterfly effect in Higher Derivative Gravities
• Null Energy Condition violations in bimetric gravity
• Bardeen variables and hidden gauge symmetries in linearized massive gravity
• Bimetric Theory and Partial Masslessness with Lanczos-Lovelock Terms in Arbitrary Dimensions
• On the Potential for General Relativity and its Geometry
• Criticality and extended phase space thermodynamics of AdS black holes in higher curvature massive gravity
• Neutron star merger GW170817 strongly constrains doubly coupled bigravity
• Consistent interactions and involution
• Infrared lessons for ultraviolet gravity: the case of massive gravity and Born-Infeld
• Mass eigenstates in bimetric theory with matter coupling
• Integrated Sachs-Wolfe effect in massive bigravity
• Higher dimensional nonlinear massive gravity
• Friction in Gravitational Waves: a test for early-time modified gravity
• On ghosts in theories of self-interacting massive spin-2 particles
• A general mass term for bigravity
• Dipolar Dark Matter with Massive Bigravity
• The Boulware-Deser mode in Zwei-Dreibein gravity
• Canonical structure of Tetrad Bimetric Gravity
• Comments About Hamiltonian Formulation of Non-Linear Massive Gravity with Stuckelberg Fields
• A new quasidilaton theory of massive gravity
• Stability and Anti-evaporation of the Schwarzschild-de Sitter Black Holes in Bigravity
• Consistent deformations of free massive field theories in the Stueckelberg formulation
• An Analysis of Characteristics in Non-Linear Massive Gravity
• Stable FLRW solutions in Generalized Massive Gravity
• More on effective composite metrics
• New proposal for non-linear ghost-free massive $F(R)$ gravity: cosmic acceleration and Hamiltonian analysis
• Linear spin-2 fields in most general backgrounds
• Cosmological viability of massive gravity with generalized matter coupling
• On stars, galaxies and black holes in massive bigravity
• Higher dimensional massive bigravity
• Misner-Sharp Mass and the Unified First Law in Massive Gravity
• Gordon and Kerr-Schild ansatze in massive and bimetric gravity
• The Maxwell-Proca theory: definition and construction
• Absence of ghost in a new bimetric-matter coupling
• Strong lensing constraints on bimetric massive gravity
• Remark About Hamiltonian Formulation of Non-Linear Massive Gravity in Stuckelberg Formalism
• Space-time Philosophy Reconstructed via Massive Nordström Scalar Gravities? Laws vs. Geometry, Conventionality, and Underdetermination
• Metric Formulation of Ghost-Free Multivielbein Theory
• Field redefinitions in theories beyond Einstein gravity using the language of differential forms
• Constraining the Schwarzschild-de Sitter Solution in Models of Modified Gravity
• Generalized massive gravity in arbitrary dimensions and its Hamiltonian formulation
• Non-Singular Black Holes in Massive Gravity: Time-Dependent Solutions
• Spatially Covariant Theories of a Transverse, Traceless Graviton, Part I: Formalism
• Dark matter scenarios with multiple spin-2 fields
• Non-minimal derivative couplings of the composite metric
• Analysis of constraints and their algebra in bimetric theory
• New massive bigravity cosmologies with double matter coupling
• Interacting spin-2 fields in the Stueckelberg picture
• Dynamical analysis of the cosmology of mass-varying massive gravity
• Partially Massless Graviton on Beyond Einstein Spacetimes
• Perturbations for massive gravity theories
• Extended Weyl Invariance in a Bimetric Model and Partial Masslessness
• Cosmology and Stability in Scalar-Tensor bigravity
• Consistent metric combinations in cosmology of massive bigravity
• Comments on (super)luminality
• Massive gravity, the elasticity of space-time and perturbations in the dark sector
• Probing correlation between photon orbits and phase structure of charged AdS black hole in massive gravity background
• Spherically symmetric analysis on open FLRW solution in non-linear massive gravity
• Bimetric-Affine Quadratic Gravity
• Extracting Bigravity from String Theory
• One-loop divergences in massive gravity theory
• Non-local formulation of ghost-free bigravity theory
• Modified-gravity theories with nondynamical background fields
• Cascading dust inflation in Born-Infeld gravity
• Fierz-Pauli theory reloaded: from a theory of a symmetric tensor field to linearized massive gravity
• Long Range Effects in Gravity Theories with Vainshtein Screening
• Self-accelerating Massive Gravity: Bimetric Determinant Singularities
• On dRGT massive gravity with degenerate reference metrics
• Insulator/metal phase transition and colossal magnetoresistance in holographic model
• Consistency of Relevant Cosmological Deformations on all Scales
• Universally Coupled Massive Gravity, III: dRGT-Maheshwari Pure Spin-$2$, Ogievetsky-Polubarinov and Arbitrary Mass Terms
• Energy-Momentum portal to dark matter and emergent gravity
• Hawking-Moss instanton in nonlinear massive gravity
• Decoherence of Gravitational Wave Oscillations in Bigravity
• Equivalent Theories Redefine Hamiltonian Observables to Exhibit Change in General Relativity
• Einstein's Equations for Spin $2$ Mass $0$ from Noether's Converse Hilbertian Assertion
• Phase transition and entropic force of de Sitter black hole in massive gravity
• Non-linear partially massless symmetry in an SO(1,5) continuation of conformal gravity
• Gauge and global symmetries of the candidate partially massless bimetric gravity
• Combining cosmological and local bounds on bimetric theory
• Properties of Bigravity Solutions in a Solvable Class
• Cutoff for Extensions of Massive Gravity and Bi-Gravity
• Mass - radius ratio bounds for compact objects in Lorentz-violating dRGT Massive Gravity theory
• Matter coupling in partially constrained vielbein formulation of massive gravity
• Hamiltonian Formalism of Bimetric Gravity In Vierbein Formulation
• On nonlocally interacting metrics, and a simple proposal for cosmic acceleration
• Coupling between Galileon and massive gravity with composite metrics
• Generalised matter couplings in massive bigravity
• New Branches of Massive Gravity
• Kaluza-Klein Reduction of Massive and Partially Massless Spin-2 Fields
• Interactions of multiple spin-2 fields beyond pairwise couplings
• Reduced Massive Gravity with Two Stückelberg Fields
• Kant, Schlick and Friedman on Space, Time and Gravity in Light of Three Lessons from Particle Physics
• Coleman-de Luccia instanton in dRGT massive gravity
• Thermodynamics of de Sitter black hole in massive gravity
• Hamiltonian Analysis of 1+1 dimensional Massive Gravity
• Exact Solution to the "Auxiliary Extra Dimension" Model of Massive Gravity
• Vainshtein Screening in Bimetric Cosmology
• Geometric Massive Gravity in Multi-Connection Framework
• A spectre is haunting the cosmos: Quantum stability of massive gravity with ghosts
• Equivalent Theories and Changing Hamiltonian Observables in General Relativity
• Cosmological histories in bimetric gravity: A graphical approach
• Hamiltonian Formalism of General Bimetric Gravity
• Is Bimetric Gravity Really Ghost Free?
• Covariant Stückelberg analysis of de Rham-Gabadadze-Tolley massive gravity with a general fiducial metric
• Structures in multiple spin-2 interactions
• Cosmic Acceleration and Growth of Structure in Massive Gravity
• Probing alternative cosmologies through the inverse distance ladder
• A Complementary Third Law for Black Hole Thermodynamics
• Causal propagation of constraints in bimetric relativity in standard 3+1 form
• Post-Newtonian parameter $\gamma$ and the deflection of light in ghost-free massive bimetric gravity
• Bouncing cosmologies in massive gravity on de Sitter
• Massive AdS Supergravitons and Holography
• Holography of information in massive gravity using Dirac brackets
• On Instability of Certain Bi-Metric and Massive-Gravity Theories
• Parameterized post-Newtonian formalism for multimetric gravity
• Bimetric Starobinsky model
• A Cosmological Study in Massive Gravity theory
• Cosmology in massive gravity with effective composite metric
• Constraints on hidden gravitons from fifth-force experiments and stellar energy loss
• Hamiltonian Formalism of Particular Bimetric Gravity Model
• Spherical dust collapse in bimetric relativity: Bimetric polytropes
• Generalising the matter coupling in massive gravity: a search for new interactions
• Homogeneous Instantons in Bigravity
• Cosmology with moving bimetric fluids
• Effective Matter Cosmologies of Massive Gravity I: Non-Physical Fluids
• Renormalizable toy model of massive spin two field and new bigravity
• New massive spin two model on curved space-time
• Strong-coupling scales and the graph structure of multi-gravity theories
• Revisiting black hole thermodynamics in massive gravity: charged particle absorption and shell of dust falling
• Complexity growth of massive black hole with a probe string
• Massive gravity, canonical structure and gauge symmetry
• On unitary subsectors of polycritical gravities
• Screened and Unscreened Solutions for Relativistic Star in de Rham-Gabadadze-Tolley (dRGT) Massive Gravity
• Aller guten Dinge sind drei: Cosmology with three interacting spin-2 fields
• Ghost-free completion of an effective matter coupling in bimetric theory
• Degravitation of the Cosmological Constant in Bigravity
• Ghost-free infinite derivative gravity
• Generalized Framework for Auxiliary Extra Dimensions
• Derivative couplings in massive bigravity
• Topological dyonic black holes of massive gravity with generalized quasitopological electromagnetism
• Non-minimal Energy-momentum squared gravity
• Hamiltonian structure of bi-gravity, problem of ghost and bifurcation
• On the absence of ghosts in quadratic bigravity
• Accelerating cosmology in modified gravity: from convenient $F(R)$ or string-inspired theory to bimetric $F(R)$ gravity
• Traversable wormholes in bi-metric gravity
• Slowly-Rotating Neutron Stars in Massive Bigravity
• Gravity with antisymmetric components
• Boulware-Deser ghost in extended quasidilaton massive gravity
• Dynamical diffeomorphisms
• Spherical symmetry in a dark energy permeated space-time
• Gravitational-wave energy and other fluxes in ghost-free bigravity
• On covariant expansion of the gravitational Stückelberg trick
• Complexity growth of BTZ black hole in massive gravity with a null string
• Stability analysis for new theories of massive spin-two particle and black hole entropy of new bigravity
• Progress and Gravity: Overcoming Divisions between General Relativity and Particle Physics and between Physics and HPS
• Hamiltonian Analysis of Minimal Massive Gravity Coupled to Galileon Tadpole Term
• Pole-skipping for massive fields and the Stueckelberg formalism
• Gravitational wave oscillations in bimetric cosmology
• Cosmological evolutions of $F(R)$ nonlinear massive gravity
• Dark Energy and Doubly Coupled Bigravity
• Dealing with ghost-free massive gravity without explicit square roots of matrices
• Axionic extension of the Proca action
• Massive graviton on arbitrary background: derivation, syzygies, applications
• Scalar Field in Massive BTZ Black Hole and Entanglement Entropy
• Modelling gravity on a hyper-cubic lattice
• On strong coupling scales in (minimal) massive gravity
• Constant Curvature Solutions of Minimal Massive Gravity
• Unusual square roots in the ghost-free theory of massive gravity
• Bi-Connected Gauss-Bonnet Gravity
• Mass spectrum and linear perturbations of ghost-free multi-spin-2 theory
• Cosmology and stability in scalar tensor bigravity with non-minimal kinetic coupling gravity
• Spherical gravitational waves and quasi-spherical waves scattered from black string in massive gravity
• The equivalence between Finsler and non-commutative geometries by massive gravity black hole
• Scalar-tensor theories with an external scalar
• Effective Matter Cosmologies of Massive Gravity: Physical Fluids
• Note About Consistent Extension of Quasidilaton Massive Gravity
• de Sitter Branes in a Flat Bulk of Massive Gravity
• Beyond dRGT - a new massive gravity theory?
• Generation of effective massive Spin-2 fields through spontaneous symmetry breaking of scalar field
• On scale-free extensions of massive (bi-)gravity
• On five-dimensional massive (bi-)gravity
• Hamiltonian structure of three-dimensional gravity in Vielbein formalism
• Gauge generator for bi-gravity and multi-gravity models
• Self-acceleration in scalar-bimetric theories
• Doubly coupled matter fields in massive bigravity
• Hamiltonian analysis and positivity of a new massive spin-2 model
• Note on Covariant Stückelberg Formalism and Absence of Boulware-Deser Ghost in Bi-gravity
• Gauss-Bonnet modification to Hawking evaporation of AdS black holes in massive gravity
• Cosmology in warped massive gravity
• Gravitational wave propagation in bigravity in the late universe
• A link between ghost-free bimetric and Eddington-inspired Born-Infeld theory
• New cosmological solutions in massive gravity theory
• 5-Dimensional Chern-Simons Gauge Theory on an Interval: Massive Spin-2 Theory from Symmetry Breaking via Boundary Conditions
• GR-GSG Hybrid Gravity
• Massive higher spin fields in curved spacetime and necessity of non-minimal couplings
• Self-interacting charged massive spin two particles in Minkowski spacetime
• Dipolar perturbations of nonbidiagonal black holes in bigravity
• A bigravity model from noncommutative geometry
• Multigravity and the cosmological constant
• Algebraic aspects of massive gravity
• Weak field limit in vierbein-Einstein-Palatini formalism and Fierz-Pauli Equation
• Effective Fluid FLRW Cosmologies of Minimal Massive Gravity
• LHC constraints on hidden gravitons
• Quantum Phase Space Description of a Cosmological Minimal Massive Bigravity Model
• Decoupling Solution Moduli of Bigravity
• Supergravity Induced Interactions on Thick Branes
• Complexity of the Einstein-Born-Infeld-Massive Black holes
• New model of massive spin two field
• Cosmological Solution Moduli of Bigravity