Massive Gravity Theories  

In General blue bullet s.a. gravity theories.
* Idea: A type of modification of general relativity in which gravitons have mass.
* History: The first linearized massive gravity theory was the Pauli-Fierz theory, which included a simple, quadratic mass term and is not considered viable because it has a ghost mode in its spectrum, with the resultant loss of unitarity of the quantum theory; Non-Pauli-Fierz theories with a generic graviton mass term and/or higher-order terms have more recently been proposed, including the dRGT non-linear massive gravity theory; 2015, Considered to be a hot topic in theoretical physics.
* Rem: Giving mass to the graviton is not as straightforward as in the case of a scalar field, since it requires the introduction of a second, fiducial metric; This modification changes the theory drastically, for example adding degrees of freedom that may alter its phenomenology and viability.
@ Intros, reviews: Hinterbichler RMP(12)-a1105; Hossenfelder blog(13)dec; de Rham LRR(14)-a1401; Mirbabayi a1412 [and perfect fluid analogy].
@ General references: Logunov TMP(94); Porrati ht/04-proc [in anti-de Sitter and Minkowski space]; Chen ap/05 [with antigravity for fermions]; Berezhiani et al JHEP(08)-a0803; de Rham PLB(10)-a0910 [non-linear realization]; Bergshoeff et al proc(11)-a1007 [and Schouten tensor, Lovelock gravity, and renormalizability]; Alberte et al JHEP(10)-a1008 [Vainshtein scale in massless limit of Higgs gravity]; Accioly et al CQG(11); Comelli et al PRD(12)-a1204 [degrees of freedom]; Baccetti et al JHEP(12)-a1206 [Gordon and Kerr-Schild Ansätze]; Burrage et al PRL(13)-a1211 [bound on graviton mass]; Deser et al PLB(13)-a1306 [acausality]; Mukohyama ed-CQG(13) [issue]; Bluhm PRD(15)-a1401 [explicit vs spontaneous diffeomorphism breaking]; Deser et al MPLA(15)-a1410 [problems]; de Rham et al CQG(15)-a1505 [uniqueness of the Einstein-Hilbert kinetic term]; Renaux-Petel a1512-proc.
@ Hamiltonian analysis: Blagojević & Cvetković JHEP(11); Banerjee et al JHEP(11) [symmetries]; Klusoň JHEP(12)-a1202, PRD(12)-a1209, IJMPA(13) [non-linear massive gravity]; Golovnev a1302-conf [ADM analysis]; Comelli et al JHEP(13)-a1305 [general analysis, possible theories]; Soloviev a1505 [and cosmology]; Mahdavian Yekta PRD(15)-a1503, De Felice & Mukohyama PLB(16)-a1506 [minimal theory]; Gabadadze & Pirtskhalava PRD(18)-a1803 [boundary terms].
@ Coupling to matter: Falkowski & Isabella a2001 [massive spin-2 field interacting with spin-0, spin-1/2, or spin-1 matter, UV properties].
@ And Higgs mechanism: Goon et al JHEP(15)-a1412 [as a Higgs phase of general relativity].
@ Quantum aspects: Park JHEP(11)-a1011 [non-Pauli-Fierz theory]; de Rham et al PRL(11)-a1011 [ghost-free, covariant non-linear theories]; de Rham et al PRD(13)-a1307 [one-loop quantum corrections]; Akagi & Mori PRD(19)-a1812 [constraints, absence of ghosts]; > s.a. Boulware-Deser Ghost; higher-order lagrangian theories.

Related Theories > s.a. 2D gravity; 3D massive gravity; bimetric gravity; conformal gravity; dRGT; Pauli-Fierz Theory [including alternative linear theories].
* Extended non-linear theory: A varying-mass generalization of non-linear massive gravity.
* Non-linear partially massless theory: A theory of massive gravity in which the spin-2 graviton has four propagating degrees of freedom, as opposed to the five polarizations of a massive theory and the two of a massless theory.
@ Non-local theory: Jaccard et al PRD(13)-a1305 [fully covariant theory without an external reference metric]; Maggiore PRD(14)-a1307 [and phantom dark energy]; Modesto & Tsujikawa PLB(13)-a1307 [generally covariant action].
@ Non-linear massive gravity: Arraut & Chelabi EPL(16)-a1603 [as a gravitational σ-model].
@ Non-linear partially massless theory: de Rham et al PRD(13)-a1302; Brito et al PRD(13)-a1306 [black holes]; Deser et al PRD(13)-a1306 [no consistent bimetric gravity?]; Alexandrov & Deffayet JCAP(15)-a1410 [3D]; Tannukij & Oh a1807 [as quantum gravity candidate].
@ Non-linear with f(R) contributions: Cai et al PRD(14)-a1307 [and cosmology].
@ Other theories: Scharf GRG(10) [massless limit is modified general relativity]; Dengiz & Tekin PRD(11)-a1104 [Weyl-invariant version of New Massive Gravity, symmetry breaking and Higgslike mechanism]; Comelli et al PRD(13)-a1302 [weak massive gravity]; Park & Sorbo JHEP(13) [from higher-derivative gravity]; Bracho & Khoudeir PRD(13) [new massive dual gravity, first-order actions]; Lin PLB(13)-a1305 [with SO(3) symmetry]; Blas & Sibiryakov JETP(15)-a1410 [Lorentz-violating UV completions]; Do PRD(16)-a1602 [higher-dimensional, non-linear]; Chamseddine & Mukhanov JHEP(18)-a1805 [mimetic, ghost-free]; Parvizi & Sadeghi EPJC-a1704 [higher-order, and holography]; Gümrükçüoğlu et al a2003 [with non-minimal coupling]; > s.a. born-infeld theory; 3D massive gravity.
> Related topics: see graviton [massive]; interactions [instantaneous]; spacetime [as an effective elastic medium].
> Online resources: see Wikipedia page.

Solutions and Phenomenology > s.a. 3D black holes; black holes in modified theories; black-hole thermodynamics.
@ General references: Tasinato et al CQG(13)-a1304 [exact solutions, rev]; Camanho et al PRD(17)-a1610 [causality constraints]; Cheung & Remmen JHEP(16)-a1601 [constraints from unitarity and analyticity of scattering amplitudes].
@ Spherically symmetric solutions: Damour et al PRD(03)ht/02; Brihaye & Verbin PRD(12)-a1109 [perfect fluid]; Sbisà et al PRD(12)-a1204; > s.a. schwarzschild-de sitter spacetime.
@ Other isolated objects: Bebronne PRD(10)-a1005 [static, quasi-linear]; Babichev et al PRD(10)-a1007 [recovery of general-relativity solutions]; Gruzinov & Mirbabayi PRD(11)-a1106 [stars and black holes]; Deser & Waldron PRD(14)-a1310 [novel effects of sources]; > s.a. types of neutron stars.
@ Astrophysical tests: Décanini et al a1401 [black hole ringings].
@ Cosmology, special solutions: D'Amico et al PRD(11)-a1108 [(no) homogeneous and isotropic solutions]; Vakili & Khosravi PRD(12)-a1204 [non-linear massive gravity, open FLRW background]; Gratia et al PRD(12) [spherically symmetric, cosmological-constant-like behavior]; Kobayashi et al PRD(12)-a1205 [with all three spatial geometries]; Martín-Moruno & Visser CQG(13)-a1301 [vacuum and non-vacuum solutions]; Solomon et al JCAP(15)-a1409 [how to produce viable cosmologies]; de Rham IJMPD(14)-a1410 [stable FLRW solutions in generalized massive gravity]; Pinho et al RMAA-a1510; De Felice & Mukohyama JCAP(16)-a1512 [minimal theory, dust-filled FLRW].
@ Cosmology, perturbations: D'Amico PRD(12)-a1206; De Felice et al PRL(12)-a1206 [instability of Bianchi I models]; De Felice et al JCAP(13)-a1303, Khosravi et al JCAP(13)-a1305 [stability of cosmological solutions]; Gümrükçüoğlu et al PRD(13)-a1304 [in extended massive gravity]; De Felice et al CQG(13)-a1304 [rev]; Nesseris & Tsujikawa PRD(14)-a1402 [observational constraints on non-local massive gravity]; Comelli et al PRD(14)-a1403, Solomon et al JCAP(14)-a1404, Lagos & Ferreira JCAP(14)-a1410 [of FLRW models, massive bigravity].
@ Cosmology, observational constraints: Cardone et al PRD(12)-a1205; Gong a1210.
@ Cosmology, in extended theories: Hinterbichler et al PLB(13)-a1301; Leon et al CQG(13)-a1301 [dynamical analysis of various scenarios].
@ Cosmology, other: Gümrükçüoğlu et al PLB(12)-a1206 [FLRW model with anisotropic perturbations]; Langlois & Naruko CQG(12), CQG(13) [on de Sitter spacetime]; Wyman et al PRD(13)-a1211; Comelli et al JCAP(14)-a1307; Heisenberg & Refregier JCAP(16)-a1604.
@ Related topics: Gratia et al CQG(13)-a1305 [and determinant singularities]; Guarato & Durrer PRD(14)-a1309 [perturbations on a general background].
> Related topics: see higgs mechanism; kaluza-klein phenomenology; Vainshtein Mechanism.

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