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In General > s.a. models in canonical
quantum gravity [including
midisuperspace]; geometrodynamics [superspace].
* Idea: Restrict the
number of degrees of freedom of the metric to a finite number, by imposing
symmetries; Consequences are that (1) The quantum constraints become easier
to handle,
when written in the usual variables; (2) Since we allow fewer metric variations
when getting the equations of motion from the action, we may get more classical
solutions, some spurious
ones being unstable; (3) Semiclassically and in quantum theory, the results
may not be equivalent to appropriate sectors of the full theory.
@ General references: Kiefer PRD(88);
Morikawa PRD(89);
Nagai PTP(89);
Guven & Vergara PRD(91);
Shabanov PLB(91);
Torre IJTP(99);
Bojowald
et al CQG(04)gq/03 [and
spin connection]; Cognola & Zerbini gq/04 [rev];
Capozziello et al CQG(08)-a0706 [tomographic
representation]; Halliwell JPCS(11)-a1108 [decoherent-histories analysis]; Barvinsky & Kamenshchik PRD(14)-a1312 [selection rules for the Wheeler-DeWitt equation]; Bojowald & Brahma PRD(16)-a1509 [as infrared contributions]; Pal & Banerjee JMP(16)-a1601 [and unitarity].
@ Limits of validity: Kuchař & Ryan PRD(89);
Sinha & Hu PRD(91)
[from quantum field theory in curved spacetime]; Mazzitelli PRD(92)
[corrections from midisuperspace]; Rovelli & Wilson-Ewing PRD(14)-a1310 [and the accuracy of the effective equations of lqc]; > s.a. semiclassical cosmology.
@ Canonical and path integral: Marolf in(95)gq/94 [spectral
analysis inner product]; Marolf PRD(96)gq;
Menotti & Peirano NPB(97)ht/96 [measure];
Simeone PLA(03); Qin & Ma PRD(12)-a1110 [coherent state functional integrals, and Moyal star product]; Christodoulakis et al JGP(13)-a1208 [and constrained symmetries].
@ Noether symmetries: Capozziello & Lambiase GRG(00)gq/99, GRG(00)gq/99; Capozziello et al EPJC(12)-a1206; Capozziello & De Laurentis a1308-proc [in extended gravity theories].
@ Related topics: Calzetta CQG(89)
[dissipation and memory loss]; Hu et al gq/93-proc
[dissipative processes]; Embacher gq/96,
NPPS(97)gq/96
[decompositions]; Krori CQG(96)
[and conformal degree of freedom]; Simeone JMP(98)gq/01 [as
gauge theory]; Cavaglià IJMPD(99)gq/98 [approximate
quantization]; Montani IJMPD(04)gq [revised
canonical quantum gravity]; Marolf PRD(09)-a0902 [observables
and problem of time].
Bianchi Models > s.a. loop quantum gravity [homogeneous and isotropic cosmologies]; semiclassical cosmology; spin-foam models.
@ Type II: Manojlović & Mena PRD(93)gq; Christodoulakis et al PLB(97); Christodoulakis & Papadopoulos PLB(01)gq/00; Christodoulakis & Papadopoulos gq/01 [and
VIA, VIIA]; Ashtekar & Wilson-Ewing PRD(09)-a0910 [lqc, singularity resolution]; Corichi & Montoya PRD(12)-a1201 [lqc, with a massless scalar field]; Bergeron et al PRD(14)-a1405; Farag Ali & Majumder CQG(14)-a1402 [with gup]; Saini & Singh CQG(17)-a1707 [lqc, singularity resolution].
@ Types III-VII: Hojman et al PRD(92)
[Hamiltonian from equations of motion]; Christodoulakis et al PRD(96)
[V], PLB(98)
[V],
PLB(01)gq [VI
and VII vacuum]; > s.a. quantum cosmology [other theories].
@ Type IX: Misner PR(69);
Kodama PRD(90);
Giampieri PLB(91);
Jensen et al NPB(91);
Louko PRD(95)gq/94 [Chern-Simons
state and Hartle-Hawking boundary conditions]; Major & Smolin PRD(95)gq/94, gq/96;
Marolf CQG(95)gq/94 [observables
and Hilbert space]; Graham & Paternoga PRD(96)gq [from
Chern-Simons state]; Paternoga & Graham
PRD(96)gq [Λ < 0];
Savchenko et al IJMPA(99)gq,
IJMPA(00)gq;
Macías
GRG(99);
Craig & Hartle PRD(04)gq/03 [generalized
sum over histories]; Kheyfets et al CQG(06)gq/05
[non-Dirac, expectation value of constraints]; Marcianò a1003-MG12 [inhomogeneities]; Bergeron et al PRD(15)-a1501 [singularity avoidance], PRD(16)-a1511 [inflationary aspects]; D'Odorico & Saueressig PRD(15)-a1511 [asymptotic safety motivated corrections, phase transition]; > s.a. quantum
cosmology [inhomogeneities].
@ Type IX, affine coherent states: Bergeron et al PRD(15)-a1501; Małkiewicz a1512-MG14.
@ Type IX, supersymmetric:
Graham PLB(92);
Graham & Bene PLB(93)
[+ scalar]; Moniz gq/95-conf, IJMPA(96)gq/95; Damour & Spindel PRD(14)-a1406.
@ Type IX, lqc: Bojowald & Date PRL(04)gq/03; Battisti et al PRD(10)-a0911 [triangulated]; Wilson-Ewing PRD(10)-a1005; Corichi & Montoya CQG(16)-a1502 [effective dynamics]; Corichi & Karami IJMPD(16)-a1605 [inverse triad corrections]; Saini & Singh a1712 [singularity resolution].
@ Chaos: Berger PRD(89)
[vacuum IX, chaotic]; Graham gq/94 [VIII
and IX]; Bojowald et al CQG(04)gq [vacuum
IX, lqg, non-chaotic behavior]; in Matinyan ht/06-MGXI;
Forte CQG(09)-a0812 [and
billiard representation]; Koehn PRD(12)-a1107 [wave packets and quantum cosmological billiards]; Lecian et al PRD(13)-a1311 [polymer representation]; > s.a. semiclassical
cosmology.
@ In lqc / lqg: Bojowald CQG(00)gq/99 [class
A], CQG(03)gq;
Bojowald et al CQG(06)gq/05 [anisotropies];
Ita
a0812 [gravity
+ Klein-Gordon], CQG-a0901
[Chang-Soo/CDJ variables]; Lamon a0909 [3-torus
space]; > s.a. FLRW
cosmology.
@ Supersymmetric, supergravity: Capovilla & Guven CQG(94)gq [class A, Ashtekar
variables]; Capovilla & Obregón PRD(94)gq [class A, with a
cosmological constant]; Socorro & Medina
PRD(00)gq/99 [class
A].
@ General class A:
Ashtekar et al gq/93; Christodoulakis et al G&C(02)gq/94 [framework];
Yamazaki gq/01 [Dirac
sqrt]; Wilson-Ewing PRD(16)-a1512 [diagonal, with self-dual variables].
@ Other models: Christodoulakis & Korfiatis JMP(92)
[with a scalar field]; Ashtekar et al IJMPD(93)gq [observables
and quantization]; Damour & Spindel PRD(11)-a1103 [with a Dirac spinor field]; > s.a. bianchi
models; bianchi I quantum cosmology [including affine quantization].
Wormholes, Baby Universes > s.a. cosmology [philosophical]; wormholes;
quantum gravity and cosmology [Hartle-Hawking
proposal].
@ Effective action, decoherence: Hájíček PRD(82), PRD(82);
Hawking PLB(87), PRD(88); Coleman & Lee PLB(89).
@ Applications: Lee PRL(88)
[scalar field and effective interaction]; Accetta et al PRD(89).
@ Baby universes: Hawking & Laflamme PLB(88) [and non-renormalizability];
Giddings & Strominger NPB(89);
Myers NPB(89);
Borde et al PRD(99)
[in monopole collisions]; Vachaspati a0705-GRF.
@ Related topics: Lyons NPB(89)
[fermions]; Volovich PLB(89)
[spacetime dimension].
Other Models and Theories > s.a. Discrete Models; non-commutative cosmology;
path integrals; quantum cosmology;
string cosmology.
* Microsuperspace: A model
in which the sum over histories reduces to a finite number of ordinary integrals.
@ References: Halliwell & Louko PRD(89)
[S4 microsuperspace];
Sawayama gq/06 [static
inhomogeneous]; > s.a.
anti-de sitter space; FLRW
models; kantowski-sachs models; models
in canonical
quantum gravity; Taub Universe.
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