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"Massive Gravity"
Claudia de Rham 
Abstract
1 Introduction
2 Massive and Interacting Fields
2.1 Proca field
2.2 Spin-2 field
2.3 From linearized diffeomorphism to full diffeomorphism invariance
2.4 Non-linear Stückelberg decomposition
2.5 Boulware–Deser ghost
I Massive Gravity from Extra Dimensions
3 Higher-Dimensional Scenarios
4 The Dvali–Gabadadze–Porrati Model
4.1 Gravity induced on a brane
4.2 Brane-bending mode
4.3 Phenomenology of DGP
4.4 Self-acceleration branch
4.5 Degravitation
5 Deconstruction
5.1 Formalism
5.2 Ghost-free massive gravity
5.3 Multi-gravity
5.4 Bi-gravity
5.5 Coupling to matter
5.6 No new kinetic interactions
II Ghost-free Massive Gravity
6 Massive, Bi- and Multi-Gravity Formulation: A Summary
7 Evading the BD Ghost in Massive Gravity
7.1 ADM formulation
7.2 Absence of ghost in the Stückelberg language
7.3 Absence of ghost in the vielbein formulation
7.4 Absence of ghosts in multi-gravity
8 Decoupling Limits
8.1 Scaling versus decoupling
8.2 Massive gravity as a decoupling limit of bi-gravity
8.3 Decoupling limit of massive gravity
8.4 Λ3-decoupling limit of bi-gravity
9 Extensions of Ghost-free Massive Gravity
9.1 Mass-varying
9.2 Quasi-dilaton
9.3 Partially massless
10 Massive Gravity Field Theory
10.1 Vainshtein mechanism
10.2 Validity of the EFT
10.3 Non-renormalization
10.4 Quantum corrections beyond the decoupling limit
10.5 Strong coupling scale vs cutoff
10.6 Superluminalities and (a)causality
10.7 Galileon duality
III Phenomenological Aspects of Ghost-free Massive Gravity
11 Phenomenology
11.1 Gravitational waves
11.2 Solar system
11.3 Lensing
11.4 Pulsars
11.5 Black holes
12 Cosmology
12.1 Cosmology in the decoupling limit
12.2 FLRW solutions in the full theory
12.3 Inhomogenous/anisotropic cosmological solutions
12.4 Massive gravity on FLRW and bi-gravity
12.5 Other proposals for cosmological solutions
IV Other Theories of Massive Gravity
13 New Massive Gravity
13.1 Formulation
13.2 Absence of Boulware–Deser ghost
13.3 Decoupling limit of new massive gravity
13.4 Connection with bi-gravity
13.5 3D massive gravity extensions
13.6 Other 3D theories
13.7 Black holes and other exact solutions
13.8 New massive gravity holography
13.9 Zwei-dreibein gravity
14 Lorentz-Violating Massive Gravity
14.1 SO(3)-invariant mass terms
14.2 Phase m1 = 0
14.3 General massive gravity (m0 = 0)
15 Non-local massive gravity
16 Outlook
Acknowledgments
References
Footnotes
Figures
The local gauge invariance associated with covariance leads to d first class constraints which remove 2d degrees of freedom, albeit in phase space. For global symmetries such as Lorentz invariance, there is no first-class constraints associated with them, and that global symmetry only removes d(d− 1)∕2 degrees of freedom. Technically, the counting should be performed in phase space, but the results remains the same. See Section 7.1 for a more detailed review on the counting of degrees of freedom.