Modified Approaches to Quantum Gravity  

In General > s.a. BF theory; clifford algebra; newton-cartan theory; Non-Symmetric Gravity; theories of gravitation.
@ Strong-coupling limit: Henneaux et al PLB(82); Pilati PRD(82); PRD(83); Francisco & Pilati PRD(85); Rovelli PRD(87); Husain CQG(88); Kakas CQG(89) [matter]; Gamboa PRL(95) [2D]; Maeda & Sakamoto PRD(96)ht [expansion]; Sakamoto PRD(09)-a0905 [renormalized, and z = 2 Lifshitz point]; > s.a. modified general relativity [classical].
@ Scalar-tensor theory: Pimentel & Mora gq/00 [Bergmann-Wagoner theory]; > s.a. renormalization.
@ Modified dynamics: Smolin CQG(92) [G → 0]; Wang JPCS(06)gq/05 [conformally symmetric]; Broda et al PLB(07) [abelian theory].
@ Other dimensions: Bjerrum-Bohr NPB(04)ht/03 [D → ]; Nieto a0704 [8D, background-independent Kaluza-Klein à la lqg]; > s.a. 2D and 3D quantum gravity; regge calculus.
> Other theories of gravity: see classical theories of gravity; Horava-Lifshitz Gravity; quantum cosmology [varying constants].

Linearized Gravity > s.a. [perturbations]; canonical and covariant quantum gravity.
@ Approaches: Ashtekar et al PRD(91) [lqg]; Grigore CQG(00)ht/99; Shojai & Shojai PS(03)gq [Bohmian approach]; Quevedo & Tafoya GRG(05)gq/04 [deformation]; Bomstad & Klauder CQG(06)gq [projection operator].
@ Ground state: Kuchar JMP(70) [canonical]; Hartle PRD(84) [Euclidean path integral].
@ Gravitons: Varadarajan PRD(02)gq [loop and Fock space]; Speziale JHEP(06)gq/05 [2-point function from spin foam, 3D model]; > s.a. quantum field theory in curved spacetime [graviton].
@ Around FRW backgrounds: Ford & Parker PRD(77); Bojowald et al PRD(08)-a0806 [in lqg].
@ Related topics: Moncrief GRG(79) [linearization instabilities]; > s.a. quantum regge calculus.

Higher-Order Theories > s.a. classical higher-order theories; covariant quantum gravity [stability of Minkowski].
* Results: It is renormalizable and asymptotically free [@ Tomboulis], but non-unitary (due to quartic terms in R2 that give ghosts in the propagators) and with H unbounded below [@ Stelle, etc].
@ General references: Mazzitelli PRD(92), Tomboulis PLB(96)ht [relationship with general relativity, and renormalization]; Asorey et al IJMPA(97); Mielke PRD(08)-a0707 [topological action]; Deser PRL(09) [3D ghost-free, UV-finite theory].
@ Renormalization: Utiyama & DeWitt JMP(62); Stelle PRD(77); Fukuma & Matsuura PTP(02); de Berredo-Peixoto & Shapiro PRD(05)ht/04 [Gauss-Bonnet term, 4–]; Chaves a0808 [with quadratic terms]; > s.a. renormalization of quantum gravity [UV fixed points].
@ Around de Sitter: Cognola et al JCAP(05)ht, Cognola & Zerbini JPA(06)in [one-loop covariant f(R) gravity].
@ In quantum cosmology: Hawking & Luttrell NPB(84); van Elst et al CQG(94)gq [R + R3 action]; Pimentel et al CQG(97) [pure R2 action]; Davis GRG(00) [string-motivated]; Fabris & Reuter GRG(00); Sanyal & Modak PRD(01)gq, CQG(02)gq/01 [R + R2 action]; Shojai & Shojai GRG(08)-a0801 [spatially flat]; Tkach MPLA(09)-a0808 [ghost-free theory and hierarchy problem].
@ FRW minisuperspace: Sanyal PLB(02)gq [Schrödinger equation and interpretation].
@ Related topics: Accioly et al IJTP(00) [propagator]; Kleidis et al PLB(02)ht [with massive scalar]; > s.a. approaches [asymptotic safety].
> Related topics: see Hierarchy Problem; path-integral quantum gravity; quantum gravity; semiclassical quantum gravity.

Approaches Based on Different Frameworks > s.a. non-commutative geometry; quantum spacetime.
* Possibilities: Modify the underlying structure, such as (i) Twistors; (ii) Algebraic approaches, quantum groups, non-commutative geometry; (iii) Finkelstein and other fundamentally quantum approaches (plexars, quantum topology); (iv) Posets, as finite spatial topologies, or as causal sets; (v) Fundamentally discrete approaches.
@ From space of histories: DeWitt & Molina-Paris MPLA(98)ht.
@ Bohm / pilot-wave theory: Shtanov PRD(96)gq/95; Goldstein & Teufel qp/99-in; Shojai PRD(99)gq, & Golshani IJMPA(98), IJMPA(98)gq/99, & Shojai CQG(04)gq/03; Santini PhD(00)gq [canonical quantum gravity]; Pinto-Neto & Santini GRG(02); Kenmoku et al CQG(02) [3D spherical]; Shojai & Shojai gq/04-in [lqg]; Shojai et al IJMPA(05)gq [Einstein universe]; Carroll TMP(07) [fluctuations and entropy]; > s.a. canonical quantum gravity.
@ And other hidden variables: 't Hooft CQG(99)gq [information dissipation].
@ And spectral geometry: Esposito 98-ht/97, ht/97-in, CM(05)ht/03-in [Euclidean]; Booss-Bavnbek et al Sigma(07)-a0708 [rev]; Kempf & Martin PRL(08)-a0708 [information theory and cutoffs].
@ Causality-based: Schorn CQG(97), CQG(97); Rainer IJTP(00)gq/97, CQG(00)gq/99 [algebraic]; Hardy gq/05, JPA(07)gq/06-in, a0804-in ["causaloids"]; Christensen & Crane JMP(05) [causal sites]; Markes & Hardy a0910 [and entropy]; > s.a. causal sets.
@ Discrete: Holfter & Paschke JGP(03)ht/02 [and Dirac operator]; Gambini & Pullin gq/05-in; > s.a. discrete spacetime.
@ Categorical: Crane ht/93, gq/00; Isham ATMP(03)gq, ATMP(03)gq, ATMP(04)gq/03; Isham qp/04-in; Baez qp/04; Raptis IJTP(06)gq/04-in, IJTP(07) [and abstract differential geometry]; Crane gq/06-in; > s.a. quantum spacetime models.
@ Relational: Corichi et al MPLA(02)gq; Dreyer gq/04; Raptis IJTP(07) ['third quantization']; Dreyer in(06)gq, PoS-a0710 [internal relativity]; Anderson a0809.
@ Deformed: Finkelstein LMP(96); Antonsen gq/97; Gavrilik gq/99-in [quantum algebras]; Vacaru a0801 [Lagrange-Finsler variables and Fedosov quantization]; > s.a. loop representation; modified theories [linearized gravity]; modified versions of general relativity.
@ Related topics: Ghosh ht/02 [use all signatures]; Siino ht/06 [algebraic]; Finkelstein IJTP(08)gq/06 [homotopy approach]; Raptis IJTP(06) [Glafka meeting, iconoclastic approaches]; Baker a0810 [using elastic solid model]; > s.a. approaches to quantum gravity; Topos Theory.

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