Modifications and Extensions of General Relativity |

**In General** > s.a. einstein's
equation [including approximations]; general relativity;
gravity 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.

* __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.

@ __Parametrizations__: Caldwell et al PRD(07)
[cosmological version of Post-Newtonian parameter]; > 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.

@ __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 [deformed general relativity]; Krasnov JHEP(15)-a1410 [parity-asymmetric]; Gálvez Ghersi et al a1711 [consistency of the constraint algebra]; Carballo-Rubio et al a1802 [minimally modified theories].

@ __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].

* __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}
– \(1\over4\)*g*_{ab}*T*];
> 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 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 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]; > 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 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 *g*_{ab} = 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 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; types of field theories ["shifted differential equations"].

> __Various types of theories__: see emergent gravity [including analog gravity]; entropic gravity; finsler geometry [including Randers]; gravity theories [including spin-2 fields in Minkowski space]; kaluza-klein theory; semiclassical quantum gravity [quantum corrections]; supergravity.

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