DeWitt Boundary Condition in One-Loop Quantum Cosmology
DeWitt’s suggestion that the wave function of the universe should vanish at the classical Big Bang singularity is considered here within the framework of one-loop quantum cosmology. For pure gravity at one loop about a flat four-dimensional background bounded by a 3-sphere, three choices of boundary...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/9/4/187 |
| _version_ | 1827743552237469696 |
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| author | Giampiero Esposito |
| author_facet | Giampiero Esposito |
| author_sort | Giampiero Esposito |
| collection | DOAJ |
| description | DeWitt’s suggestion that the wave function of the universe should vanish at the classical Big Bang singularity is considered here within the framework of one-loop quantum cosmology. For pure gravity at one loop about a flat four-dimensional background bounded by a 3-sphere, three choices of boundary conditions are considered: vanishing of the linearized magnetic curvature when only transverse-traceless gravitational modes are quantized; a one-parameter family of mixed boundary conditions for gravitational and ghost modes; and diffeomorphism-invariant boundary conditions for metric perturbations and ghost modes. A positive <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ζ</mi><mo>(</mo><mn>0</mn><mo>)</mo></mrow></semantics></math></inline-formula> value in these cases ensures that, when the three-sphere boundary approaches zero, the resulting one-loop wave function approaches zero. This property may be interpreted by saying that, in the limit of small three-geometry, the resulting one-loop wave function describes a singularity-free universe. This property holds for one-loop functional integrals, which are not necessarily equivalent to solutions of the quantum constraint equations. |
| first_indexed | 2024-03-11T04:28:36Z |
| format | Article |
| id | doaj.art-efb4cc7483a249ca91fa8397376918c7 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-11T04:28:36Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-efb4cc7483a249ca91fa8397376918c72023-11-17T21:40:29ZengMDPI AGUniverse2218-19972023-04-019418710.3390/universe9040187DeWitt Boundary Condition in One-Loop Quantum CosmologyGiampiero Esposito0Dipartimento di Fisica “Ettore Pancini”, Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126 Napoli, ItalyDeWitt’s suggestion that the wave function of the universe should vanish at the classical Big Bang singularity is considered here within the framework of one-loop quantum cosmology. For pure gravity at one loop about a flat four-dimensional background bounded by a 3-sphere, three choices of boundary conditions are considered: vanishing of the linearized magnetic curvature when only transverse-traceless gravitational modes are quantized; a one-parameter family of mixed boundary conditions for gravitational and ghost modes; and diffeomorphism-invariant boundary conditions for metric perturbations and ghost modes. A positive <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ζ</mi><mo>(</mo><mn>0</mn><mo>)</mo></mrow></semantics></math></inline-formula> value in these cases ensures that, when the three-sphere boundary approaches zero, the resulting one-loop wave function approaches zero. This property may be interpreted by saying that, in the limit of small three-geometry, the resulting one-loop wave function describes a singularity-free universe. This property holds for one-loop functional integrals, which are not necessarily equivalent to solutions of the quantum constraint equations.https://www.mdpi.com/2218-1997/9/4/187quantum cosmologyboundary conditionsstrong ellipticityspectral ζ-function |
| spellingShingle | Giampiero Esposito DeWitt Boundary Condition in One-Loop Quantum Cosmology Universe quantum cosmology boundary conditions strong ellipticity spectral ζ-function |
| title | DeWitt Boundary Condition in One-Loop Quantum Cosmology |
| title_full | DeWitt Boundary Condition in One-Loop Quantum Cosmology |
| title_fullStr | DeWitt Boundary Condition in One-Loop Quantum Cosmology |
| title_full_unstemmed | DeWitt Boundary Condition in One-Loop Quantum Cosmology |
| title_short | DeWitt Boundary Condition in One-Loop Quantum Cosmology |
| title_sort | dewitt boundary condition in one loop quantum cosmology |
| topic | quantum cosmology boundary conditions strong ellipticity spectral ζ-function |
| url | https://www.mdpi.com/2218-1997/9/4/187 |
| work_keys_str_mv | AT giampieroesposito dewittboundaryconditioninoneloopquantumcosmology |