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);
Vilenkin AIP(99)gq/98;
Avramidi & Esposito gq/99-conf;
Tipler ap/01 [unique
initial state]; Coule CQG(05)gq/04 [rev];
Page ht/06-MGXI;
Maydanyuk EPJC(08)-a0707; Jalalzadeh & Moniz PRD(14)-a1403 [boundary proposals and the algebra of Dirac observables].

@ __In lqg__: Bojowald GRG(03)gq;
Bojowald & Vandersloot PRD(03)gq, gq/03-MGX;
Coule gq/03 [comparison];
> s.a. signature change.

@ __Phenomenology__: Suenobu & Nambu GRG(17)-a1603 [numerical solution of the WDW equation, and inflationary number of e-foldings].

@ __For perturbations__: Giovannini CQG(03).

**Universe-from-Nothing Proposals** > s.a. hartle-hawking no-boundary proposal.

* __Vilenkin's tunneling
wavefunction__: 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,
IJMPD(10); Blanco-Pillado et al JCAP(12); He et al PRD(14)-a1404 [argument from explicit solution of the Wheeler-DeWitt equation]; Kohli a1405 [comments on Krauss' book];
Battarra & Lehners PLB(15)-a1406 [in ekpyrotic cosmological theories].

@ __From tunneling__: Kandrup & Mazur IJMPA(91)
[semiclassical, rev]; Labraña PRD(12)-a1111; Feldbrugge et al a1705 [semi-classical description untenable].

@ __And the cosmological constant__: Coule MPLA(95)gq/94;
Barvinsky & Kamenshchik PRD(06)ht.

@ __And inflation__: Vilenkin PRD(98)gq, gq/02-proc
[vs Hartle-Hawking proposal]; Coule & Martin PRD(00)
[open universe].

> __Related topics__: see inflation and planck-scale physics; gravitational instantons; Nothing.

**Other Proposals** > s.a. Penrose's Weyl Curvature Hypothesis.

* __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-MGXI [thermal
boundary conditions].

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2017