Hartle-Hawking No-Boundary Quantum Cosmology  

In General > s.a. cosmological-constant problem; quantum cosmology.
* Idea: Choose the set of histories C to consist of Euclidean four-geometries with no past boundary (empty beginning and smooth fields) in

\(\Psi[g_{ij}, t, \phi]\):= ∫C \(\cal D\)gij \(\cal D\)φ exp{−I[gij, φ]} .

* Limitations: 1990, 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 from 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]; Page JCAP(07)ht/06 [re Susskind's challenge]; Wu MPLA(11) [rev]; Feldbrugge et al PRL(17)-a1705 [semi-classical description untenable]; Feldbrugge et al PRD(18)-a1708 [problem]; Bojowald & Brahma PRL(18)-a1810 [proposal rescued by dynamical signature change in loop quantum cosmology]; Halliwell et al PRD(19)-a1812 [without functional integrals]; Di Tucci & Lehners PRL(19)-a1903 [as a path integral with Robin boundary conditions]; Alexander et al CQG(21)-a2012 [generalization beyond minisuperspace]; Partouche et al a2105 [gauge fixing and field redefinitions].
@ In Lorentzian quantum cosmology: Diaz Dorronsoro et al PRD(17)-a1706; Di Tucci et al PRD(19)-a1911.
@ 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); Fujio & Futamase PRD(09)-a0906 [emergence of classical mixmaster universe]; > s.a. CMB anisotropies.

Specific Theories and Models
@ 2+1 gravity: Carlip PRD(92) [approximations to action]; Carlip CQG(05)gq [real tunneling geometries].
@ In other theories: Kapetanakis et al NPB(95) [Einstein-Yang-Mills]; Csordás & Graham PLB(96) [supersymmetric]; Sarangi & Tye ht/06 [string cosmology]; Hawking & Hertog PRD(06) + pw(06)jun [and string landscape, top-down]; Hwang et al CQG(12)-a1107 [scalar-tensor gravity]; Sasaki et al CQG(13)-a1307 [massive gravity]; Battarra & Lehners JCAP(14)-a1407 [ekpyrotic and cyclic cosmologies]; Jonas & Lehners PRD(20)-a2008 [and higher-order quantum gravity corrections].
@ In specific approaches: Glaser & Surya a1410 [2D causal set quantum gravity]; Dhandhukiya & Sahlmann PRD(17)-a1608, Brahma & Yeom PRD(18)-a1808 [lqg/lqc].
@ Specific model spacetimes: Janssen et al PRD(19)-a1904 [biaxial Bianchi IX minisuperspace].
@ Real tunneling solutions: Carlip CQG(93)gq; Embacher GRG(96) [and spacetime dimensionality].
@ Perturbations: Green & Unruh gq/02; Hartle et al PRD(10) [single scalar field perturbations, eternal inflation]; Diaz Dorronsoro et al PRL(18)-a1804 [damping, stable to perturbations]; Feldbrugge et al a1805 [inconsistencies]; Di Tucci & Lehners PRD(18)-a1806 [unstable].
@ 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]; Clunan a0704 [and effective potential]; Hartle et al PRD(08)-a0802, PRL(08)-a0711 [semiclassical]; Rajeev et al a2101 [bouncing model analogue and Lorentzian path-integral representation].
> Related topics: see AdS spacetime; arrow of time; gravitational instantons; inflation and planck-scale physics.

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