Modifications and Extensions of General Relativity  

In General > s.a. einstein's equation [including approximations]; general relativity; gravity theories [types of theories]; physics [visions]; quantum gravity.
* Motivation and consequences: Some modifications and extensions are motivated by quantum gravity, others by attempts to explain observations at cosmological scales; Theories that modify gravity at large scales may be incompatible with solar-system tests, and screening mechanisms have been devised to avoid running into this difficulty.
* Types of modified dynamics: Some modified theories preserve general covariance (e.g., higher-order theories), others don't (e.g., hořava's).
* Types of modified frameworks: Examples are based on non-commutative gravity; Octonions; Topos Theory.
* Extensions: The theory can be extended to complex, degenerate or otherwise singular metrics, or signature-changing ones.
* Minimally modifed gravity: A class of non-linear 4D gravitational theories with two local degrees of freedom; Their construction relies on the breaking of 4D diffeomorphism invariance while preserving the 3D diffeomorphism symmetry.
* Neighbors of general relativity: (Bengtsson's term) A class of theories obtained by using a tetrad e (or related quantities such as a 2-form B in BF-type theories) and a connection A as variables, plus possibly additional ones to implement constraints, and introducing continuous parameters that deform the theory away from general relativity; They were initially studied in the Hamiltonian formulation, Krasnov introduced their Lagrangian formulation, and Smolin suggested the enlargement of the gauge group.
@ Limits of the theory: Tavakol & Zalaletdinov FP(98)gq/97; Ahluwalia MPLA(98)gq, gq/98-proc; Okorokov gq/99; Chapline et al IJMPA(03)gq/00 [black hole event horizon]; Ishak et al PRD(06)ap/05 [from cosmic acceleration]; Bertolami IJMPD(09)-a0905-GRF [and cosmological constant]; Afshordi BASI-a1203; Linder a2003 [special limiting cases and phenomenology].
@ Approaches: Caldwell et al PRD(07) [cosmological version of Post-Newtonian parameter]; Heisenberg PRP(19)-a1807; > s.a. modified newtonian gravity.
@ Constraints, phenomenology: Aguirre et al CQG(01)hp; Mortlock & Turner MNRAS(01)ap [from lensing]; Barausse & Sotiriou PRL(08)-a0803 [Kerr perturbations]; Skordis PRD(09)-a0806 [and cosmology]; Berkhahn et al PRL(12)-a1106 [stable, viable deformation]; > s.a. cosmology in modified theories; tests of general relativity.
@ Minimally modified gravity: Lin & Mukohyama JCAP(17)-a1708; Carballo-Rubio et al JCAP(18)-a1802; Mukohyama & Noui a1905 [Hamiltonian approach].
@ Neighbors / deformations of general relativity: Bengtsson JMP(91) [action, metric]; Bengtsson & Boström CQG(92); Bengtsson & Peldán IJMPA(92); Capovilla NPB(92); Bengtsson CQG(93), GRG(96)gq/95 [connection and curvature]; Krasnov PRL(08)-a0711 [deformations of Ashtekar constraint algebra]; Kong PLB(08); Shalyt-Margolin a1003 [and generalized uncertainty principle]; Dvali et al PRD(11)-a1006 [constraints on trans-Planckian gravity]; Bojowald & Paily PRD(13)-a1212, comments Balek & Lecian a1810 [deformed general relativity]; Krasnov JHEP(15)-a1410 [parity-asymmetric]; Gálvez Ghersi et al a1711 [consistency of the constraint algebra]; Cuttell PhD(19)-a1910; Krasnov & Mitsou a2012 [complex–geometrodynamics and reality conditions].
@ Strong-coupling limit: Isham PRS(76), in(84); Pilati in(82); Tsacoyeanes PRD(87); Goldberg GRG(88); Helfer et al GRG(88); Salopek CQG(98)gq, CQG(99)gq/98 [applications]; Frasca IJMPD(06)ht/05 [expansion, vacuum ADM formalism]; > s.a. initial-value formulation; quantum version.

Other Modifications > s.a. conformal invariance; quasilocal theory; non-local theories; theories with extended signatures [including degenerate].
* Quantum-gravity motivated: Modifications of general relativity motivated by quantum gravity include effectve higher-order ones from renormalization-induced terms in the action, and energy-dependent metrics as in rainbow gravity.
* Time-asymmetric extensions: A class of modified gravity theories that deform general relativity in a way that breaks time reversal invariance and, very mildly, locality; The algebra of constraints, local physical degrees of freedom, and their linearized equations of motion, are unchanged.
@ Cosmological constant as integration constant: Padmanabhan IJMPD(06)gq; Afshordi a0807 [matter source \(T^~_{ab}\) − \(1\over4\)gabT]; > s.a. unimodular relativity.
@ With varying constants: Barrow et al PLB(02)ap [G and α]; Franzmann a1704 [covariant approach and cosmological applications].
@ Infrared modifications: Piazza IJMPD(09)-a0904-GRF, NJP(09)-a0907 [and "ultra-strong equivalence principle"]; Gao PLB(10)-a0905 [UV and IR, f(R) and K-essence gravity, ADM formalism]; Nesseris et al PLB(10)-a0910 [and cosmological acceleration]; Iorio JCAP(11)-a1012 [solar-system constraints]; Grumiller & Preis IJMPD(11)-a1107 [Rindler force]; Iorio MNRAS(12)-a1108 [Rindler force and the Oort Cloud]; Brito et al PRD(14)-a1409 [non-linear dynamical stability]; Khosravi PRD(16)-a1606 [ensemble-averaged gravity]; > s.a. cosmology with higher-order theories; gauge theories of gravity [SO(4,2)].
@ Time-asymmetric extensions: Cortês et al PRD(15)-a1503 [proposal]; Leon & Saridakis JCAP(15)-a1504 [cosmology]; Cortês et al PRD(16)-a1606 [cosmological signatures].
@ Diffeomorphism-breaking theories: Pons & Talavera PRD(10)-a1003 [phase-space structure]; Blanchet & Marsat PRD(11)-a1107 [with a preferred time foliation with "khronon" vector field, like a hypersurface-orthogonal Einstein-aether theory]; Soo & Yu PTEP(14)-a1201, Gao PRD(14)-a1409 [with spatial diffeomorphism invariance only]; Nash GRG(19)-a1904 [and dark energy]; > s.a. hořava-lifshitz gravity.
@ With Lagrange multipliers: Capozziello et al PLB(10)-a1004 [and dark energy]; Klusoň CQG(11) [Hamiltonian analysis]; > s.a. unimodular relativity.
@ Other quantum-gravity motivated: Magueijo & Smolin CQG(04) [energy-dependent metric, "doubly general relativity"]; Bodendorfer et al PRD(18)-a1703 [with a limiting curvature, and loop quantum gravity]; > s.a. Gravity's Rainbow.
@ Related topics: Brodbeck et al JMP(99)gq/98 [as part of larger theory]; Gambini & Pullin PRL(00)gq, CQG(00)gq [from Λ → ∞ limit]; Piron FP(05); Bañados CQG(07)ht [with gab = 0 ground state]; Broda et al PLB(07)gq [abelian]; Verozub AdP(08)-a0801 [invariant under geodesic mappings]; Farkas & Martinec JMP(11)-a1002 [from an extension of spatial diffeomorphisms]; Nojiri & Odintsov PLB(10)-a1004 [covariant, renormalizable]; Deruelle & Sasaki proc(11)-a1007 [veiled general relativity]; Ellis et al CQG(11)-a1008 [trace-free Einstein equation and the cosmological constant]; Escalante IJTP(09)-a1107, Varadarajan PRD(18)-a1802 [G → 0 limit]; Heller et al CJP(13)-a1301 [from a generalization of the derivative concept]; Pani et al PRD(13)-a1306 [with non-dynamical auxiliary fields]; Chamseddine & Mukhanov JHEP(13)-a1308 [with (anti-)de Sitter tangent group]; Balitsky & Kiselev GRG(14) [with a critical acceleration].
> Related topics: see singularities [extending the spacetime]; string theory; black holes in modified theories; types of field theories ["shifted differential equations"].
> Various types of theories: see differential geometry [area-metric spacetimes]; emergent gravity [including analog gravity]; entropic gravity; finsler geometry [including Randers]; gravity theories [including spin-2 fields in Minkowski space]; kaluza-klein theory; quantum cosmology models [compact phase space gravity]; semiclassical quantum gravity [quantum corrections]; supergravity.

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