Boundary Conditions in Quantum Cosmology  

In General > s.a. quantum cosmology [Lorentzian].
* Requirements: Existence of a classical world (the density matrix must 'decohere' to get classical probabilities); Homogeneity, isotropy, right spectrum of fluctuations, enough inflation.
* Some possibilities: In addition to the ones below, proposals include Penrose's Weyl Tensor Proposal; Brout, Englert (cooperative process) Fischler, Susskind; Narlikar-Padmanabhan; Tipler's Explosion from Nothing.
@ General references: Hartle in(86); Zhuk CQG(88); Moss & Poletti NPB(90); Kandrup & Mazur IJMPA(91) [as tunneling, semiclassical, rev]; Vilenkin gq/98-in; Avramidi & Esposito gq/99-in; Tipler ap/01 [unique initial state]; Coule CQG(05)gq/04 [rev]; Page ht/06-in; Maydanyuk a0707.
@ In lqg: Bojowald GRG(03)gq; Bojowald & Vandersloot PRD(03)gq, gq/03-in; Coule gq/03 [comparison].
@ For perturbations: Giovannini CQG(03).

Hartle-Hawking Wavefunction > s.a. inflation; gravitational instanton.
* Idea: Choose C to consist of four-geometries with no past boundary (empty beginning and smooth fields) in

[gij, t, ]:= C gij exp{–I[gij, ]} .

* Limitations: Thought to give too little inflation (but see Grishchuk & Rozhansky).
* Susskind's challenge: The Hartle-Hawking no-boundary proposal should most likely lead to a nearly empty large de Sitter universe, rather than to early rapid inflation; Even if one adds the condition of observers, they are most likely to form by quantum fluctuations in de Sitter and therefore not see the structure that we observe.
@ General references: Hartle & Hawking PRD(83); Hawking NPB(84), PS(87), in(89); Laflamme & Shellard PRD(87); Louko CQG(88); Barvinsky & Kamenshchik CQG(90); Grishchuk & Rozhansky PLB(90) [and conditions for inflation]; Halliwell & Hartle PRD(90); Wu 93; Coule MPLA(95)gq/94 [and the cosmological constant]; Hawking & Hertog PRD(06) + pw(06)jun [and string landscape, top-down]; Page JCAP(07)ht/06 [re Susskind's challenge].
@ And spacetime topology: Wu PRD(85); Gurzadyan & Kocharyan JETP(89); Gibbons & Hartle PRD(90); Gibbons CQG(98); Anderson et al CQG(04)gq/03 [peaks from sum over topologies].
@ And spacetime anisotropy: Hawking & Luttrell PLB(84); Duncan & Jensen NPB(89).
@ 2+1 gravity: Carlip PRD(92) [approximations to action]; Carlip CQG(05)gq [real tunneling geometries].
@ Other theories: Kapetanakis et al NPB(95) [Einstein-Yang-Mills]; Csordás & Graham PLB(96) [supersymmetric]; Sarangi & Tye ht/06 [string cosmology].
@ Real tunneling solutions: Carlip CQG(93)gq; Embacher GRG(96) [and spacetime dimensionality].
@ Related topics: Hawking & Wu PLB(85) [with massive scalar or R2, numerical]; Page CQG(90) [age of universe], PRD(97)gq [size of the universe]; de Oliveira & Soares PRD(99) [homoclinic structure]; Green & Unruh gq/02 [perturbations]; Huang ht/05/NPB [chaotic inflation]; Clunan a0704 [and effective potential]; Hartle et al PRD(08)-a0802, PRL(08)-a0711 [semiclassical]; > s.a. AdS spacetime.

Vilenkin's Tunneling Wavefunction (Universe from nothing) > s.a. inflation; gravitational instanton.
* Idea: Solve the Wheeler-DeWitt equation imposing that the wave function have only outgoing waves on the singular boundary of superspace.
@ General references: Vilenkin PLB(82), PRD(83); Zel'dovich & Starobinskii (84); Grishchuk (84); Vilenkin PRD(84), PRD(86), PRD(94)gq; Garriga & Vilenkin PRD(97)gq/96 [pair production]; Berman & Trevisan gq/01/PRL.
@ And the cosmological constant: Coule MPLA(95)gq/94; Barvinsky & Kamenshchik PRD(06)ht.
@ And inflation: Vilenkin PRD(98)gq, gq/02-in [vs Hartle-Hawking proposal]; Coule & Martin PRD(00) [open universe].

Other Proposals
* Linde's continuous regeneration: The Hartle–Hawking and tunneling wave functions are seen as approximations valid in some regimes; a modified inflation with continuous generation of bubbles (with different dimensionality, physical constants, ...) is the thing.
@ Mixed state from Euclidean quantum gravity: Barvinsky & Kamenshchik JPA(07) [quasi-thermal state].
@ Related topics: Conradi PRD(92); Bouhmadi-Lopez & Vargas Moniz gq/07-in [thermal boundary conditions].

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