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]; Magueijo PRD(20)-a2005 [equivalence between some boundary conditions in minisuperspace].
@ 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 [black hole pair production]; Berman & Trevisan IJMPD(10)gq/01; 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]; Dąbrowski & Larsen PRD(95)gq [FLRW]; Labraña PRD(12)-a1111; Feldbrugge et al PRL(17)-a1705 [semi-classical description untenable]; Vilenkin & Yamada PRD(18)-a1808 [three approaches]; Vilenkin & Yamada PRD(19)-a1812 [the backreaction problem]; Matsui a2102 [Lorentzian path integral and WKB approximation]; > s.a. CMB anisotropies.
@ And the cosmological constant: Coule MPLA(95)gq/94; Barvinsky & Kamenshchik PRD(06)ht; Ambjørn & Watabiki MPLA(17)-a1709 [based on a W\(_3\) symmetry].
@ 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].

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at – modified 23 feb 2021