Theories of Gravitation  

Metric Theories > s.a. gravitation [gravitational theories in general, other types]; higher-order and modified theories; non-local theories.
* General relativity: Currently the standard theory of gravity; > see general relativity, its actions and variants.
@ General references: Gupta RMP(57); in Schrödinger 63; De Alfaro et al NCB(80); Mann CQG(84), CQG(89); Capozziello & De Laurentis PRP(11)-a1108; Myrzakulov et al IJMPA(13)-a1302 [general aspects of modified gravity theories]; Baykal EPJP(13)-a1310 [variational derivatives of actions]; de Rham et al CQG(14)-a1311 [no new Lorentz-invariant ghost-free kinetic interactions in 4D]; Sbisà PhD-a1406; Cayuso et al PRD(17)-a1706 [fixing the dynamics].
@ With preferred frame: Petry GRG(79); Schmelzer gq/96, gq/96; Kohler GRG(00)gq/99 [semi-teleparallel]; Eling & Jacobson PRD(04)gq/03 [dynamical]; > s.a. einstein-æther gravity; hořava gravity; modified lorentz symmetry.
@ Variable c: Magueijo PRD(00)gq, PRD(01)ap/00; > s.a. relativistic cosmology; variation of constants.
@ Scale-invariant: Kelleher CQG(04)gq/03, CQG(04)gq/03, PhD(03)gq [spatially]; Verma gq/05; Darabi IJTP(10)-a0907; Jain et al CQG(11)-a1105 [with a scalar field, stability around FLRW models]; Padilla et al PRD(14)-a1312 [generalized]; Rinaldi EPJP(18)-a1808 [non-equivalence of Jordan and Einstein frames]; > s.a. conformal gravity; Scale Invariance.
@ Other: Visser GRG(98)gq/97 [background metric]; Drummond gq/99 [variable lightcone]; Anderson gq/99 [cosmological stress tensor]; Magueijo & Smolin CQG(04)gq/03 ["doubly general"]; Jackiw & Pi PRD(03)gq [with Chern-Simons-like term]; Schuller & Wohlfarth NPB(04) [with bounds on sectional curvatures]; Roscoe ap/04/CQG [relational]; Deser CQG(06)gq [with non-degeneracy as field equation]; Di Mauro et al IJGMP(10) ["further extended theories"]; van de Meent PhD-a1111 [piecewise flat]; Lin & Mukohyama JCAP(17)-a1708 [with 2 local degrees of freedom]; Shuler EPJP(18).
Other theories: see born-infeld theory; gravitational constant [variable \(G\)]; mach's principle; massive gravity; Relativistic Theory of Gravitation.
Modified frameworks: see finsler geometry; modified lorentz symmetry.
> With additional variables: see bimetric theories; fifth force; Metric-Affine Theories; Mimetic Gravity; scalar-tensor theories; TeVeS.

Connection Theories > s.a. 3+1 connection formulation of general relativity; gauge theories of gravity.
@ References: Jakubiec & Kijowski JMP(89) [non-symmetric]; Aldrovandi et al gq/98v1; Alexandrov CQG(00)gq [SO(4, \(\mathbb C\)) lqg]; Kaul & Sengupta PRD(12)-a1006, Sengupta JPCS(12) [with Nieh-Yan, Pontryagin and Euler topological terms]; Minguzzi Symm(14)-a1403 [U(2) connection]; Castillo-Felisola & Skirzewski RMF-a1410; Licata et al IJMMP(17)-a1706 [commutator algebra of covariant derivatives]; Barbero et al JHEP(19)-a1906 [Pontryagin model on manifolds with boundary].
> Related topics: see action for general relativity [Nieh-Yan density, etc]; Affine Gravity; BF theories; Topological Gravity.

Theories with Other Variables > s.a. einstein-cartan theory; newton-cartan theory; Non-Symmetric Gravity; Scalar Theory; string theory.
* C-theory: A unified framework to study metric, metric-affine and more general theories of gravity.
@ W-gravity: Hull CMP(93)ht/92; Castro JGP(00)ht/98 [from Fedosov quantization]; Abreu et al PRD(02)ht.
@ Spinors, Dirac operator: Landi & Rovelli PRL(97)gq/96, MPLA(98)gq/97, Landi gq/99-talk [eigenvalues]; Holfter & Paschke JGP(03)ht/02 [moduli space, path integrals]; Hebecker & Wetterich PLB(03)ht [higher-dimensional], Wetterich PRD(04)ht/03; Moffat gq/03 [and the cosmological constant]; Novello gq/06 [gravity as effective theory]; Carone et al CQG(19)-a1812 [interacting fermions with massless composite graviton].
@ Scalar-vector theories: Goenner & Leclerc gq/00/PRD; Fleury et al JCAP(14)-a1406 [stability and causality].
@ Scalar-vector-tensor: Moffat JCAP(06)gq/05; Charmousis et al JHEP(12)-a1206 [higher-derivative]; Heisenberg JCAP(18)-a1801; Kase & Tsujikawa JCAP(18)-a1805 [dark energy]; Ghaffarnejad & Dehghani EPJC(19)-a1906 [galaxy rotation curves]; Liu et al a1912 [gravitational waves]; > s.a. black-hole thermodynamics; gravitomagnetism.
@ Vector theories: Borodikhin G&C(11)-a0802 [and solar-system tests]; Svidzinsky a0904 [vector theory, no black holes]; Guendelman IJMPA(10)-a0911 [vector field giving dynamical time]; Faddeev a0911 [10 vectors]; Borodikhin a1104 [quantization, renormalizable]; Svidzinsky PS(17)-a1511 [and dark energy], PS(17)-a1703 [gravitational-wave interferometer tests]; Allen PRD(18)-a1801 [gravitational-wave detection].
@ Vector-tensor theories: Yoshida & Shiraishi PS(91)-a1412 [and cosmology]; Jiménez & Maroto JCAP(09)-a0811 [viability], PRD(09)-a0905 [cosmological evolution]; Dale & Sáez ASS(12)-a1011 [viability]; Gao PRD(12)-a1111 [generalized Lorentz gauge condition]; Dale & Sáez PRD(14)-a1404 [cosmology]; Exirifard a1404-GRF [with gauge fields]; Dale et al ASS(15)-a1509 [horizons]; Kimura et al JCAP(17)-a1608 [propagating degrees of freedom]; Dale & Sáez JCAP(17)-a1610 [cosmology]; Baker et al PRL(17)-a1710 [constraints from GW170817]; Kase et al PRD(18)-a1711 [neutron stars]; Kase et al PLB(18)-a1803 [extended].
@ People with their own theories: Havel 03.
@ Self-interacting spinor fields: Novello & De Lorenci MPLA(95); Sokołowski IGJMP(07)gq [and gravitational energy]; Novello & Borba G&C(11).
@ Higher-spin gravity: Bekaert et al RMP(12)-a1007; Boulanger & Sundell JPA(11)-a1102 [action principle]; Sezgin & Sundell JHEP(12)-a1103 [geometry and observables]; Setare & Adami NPB(16)-a1601 [spin-3 topologically massive gravity, conserved charges]; Aros et al JHEP(18)-a1712 [FLRW]; Arias et al a1712 [any dimensionality, dynamical two-form]; Skvortsov et al a1805 [chiral theory]; Sharapov & Skvortsov NPB(19)-a1901 [all formally consistent field equations]; Tran a2008-PhD; > s.a. 2D gravity; 3D gravity.
@ Torsion, non-metricity: Hammond GRG(99) [2-form, torsion]; Beltrán Jiménez et al a1903; Alexander et al PRD(19)-a1905 [with dynamical cosmological constant]; > s.a. affine connections [non-metricity].
@ Other proposals: Alvarez et al PLB(92), PLB(93) [2-point distance]; Østvang PhD(01)gq, G&C(05)gq/01, G&C(07)gq/02 [quasi-metric gravity]; Mensky G&C(02)gq [in terms of paths in Minkowski space]; Bengtsson MPLA(07)gq; Fernández & Rodrigues in(10)-a0909 [distorted Lorentz vacuum]; Nash JMP(10); Trencevski et al IJTP(10) [antisymmetric tensor in Minkowski spacetime]; Koivisto PRD(11) [C-theory, post-Newtonian approach]; Böhmer & Tamanini FP(13)-a1301; Krishnan a1409 [arbitrary-rank symmetric tensors].
> Related topics: see Barker's Theory; differential geometry [area-metric spacetimes]; forms [volume form]; Designer Gravity; fractals in physics [multi-scale gravity]; Gauss-Bonnet Gravity; Ghost Fields; Hypergravity; lorentzian geometry [gravity analogs]; Matroids; non-commutative gravity; Supermanifolds; types of field theories [daor fields]; unified theories [including Weyl's]; Unparticles [ungravity]; Yilmaz Theory.
> General relativity in different variables: see canonical general relativity; formulations of general relativity [including connection, embedding, null surfaces]; lattice gravity; regge calculus.

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