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.

* __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.

@ __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.

@ __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].

@ __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 \(T^~_{ab}\)
− \(1\over4\)*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 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 *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 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 mdofied 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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