"Massive Gravity"
Claudia de Rham 
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

List of Figures

View Image Figure 1:
Spectral representation of different models. (a) DGP (b) higher-dimensional cascading gravity and (c) multi-gravity. Bi-gravity is the special case of multi-gravity with one massless mode and one massive mode. Massive gravity is the special case where only one massive mode couples to the rest of the standard model and the other modes decouple. (a) and (b) are models of soft massive gravity where the graviton mass can be thought of as a resonance.
View Image Figure 2:
Codimension-2 brane with positive (resp. negative) tension brane leading to a positive (resp. negative) deficit angle in the two extra dimensions.
View Image Figure 3:
Seven-dimensional cascading scenario and solution for one the metric potential Φ on the (5 + 1)-dimensional brane in a 7-dimensional cascading gravity scenario with tension on the (3 + 1)-dimensional brane located at y = z = 0, in the case where M 4∕M 3= M 5∕M 4 = m 6 5 7 6 7. y and z represent the two extra dimensions on the (5 + 1 )-dimensional brane. Image reproduced with permission from [149], copyright APS.
View Image Figure 4:
Degrees of freedom for massive gravity on a maximally symmetric reference metric. The only theoretically allowed regions are the upper left green region and the line m = 0 corresponding to GR.
View Image Figure 5:
Difference between phase, group, signal and front velocities. At t = δt, the phase and group velocities are represented on the left and given respectively by v = δx ∕δt phase P and vgroup = δxG ∕δt (in the limit δt → 0.) The signal and front velocity represented on the right are given by vsignal = δxS ∕δt (where δxS is the point where at least half the intensity of the original signal is reached.) The front velocity is given by vfront = δxF∕δt.
View Image Figure 6:
Polarizations of gravitational waves in general relativity and potential additional polarizations in modified gravity.
View Image Figure 7:
Alternative ways in deriving the cosmology in massive gravity.