Quantum cosmological singularities
Abstract
The problem of gravitationally induced spacetime collapse is studied in the framework of quantum cosmology. We find that whether quantum collapse occurs is effectively predetermined, on the classical level, by the choice of time. The crucial distinction is between "fast" and "slow" times, that is, between times which give rise to complete or incomplete classical evolution, respectively. We conjecture that unitary slow-time quantum dynamics is always nonsingular, while unitary fast-time quantum dynamics inevitably leads to collapse. These contentions are supported by an analysis of the dust-filled Friedmann-Robertson-Walker universes in two choices of time: a cosmic time defined by the velocity potential for the dust and an intrinsic time linked to the expansion. Indeed, these quantum models avoid the classical singularity in the slow matter-time gauge but collapse in the fast geometric-time gauge. We also investigate the qualitatively different forms---unitary and contractive---that the slow-time quantum evolution may take and explore their implications regarding quantum singularity avoidance. One surprising result is that, contrary to widespread belief, this phenomenon does not depend upon the choice of boundary conditions.
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Wheeler-DeWitt wavefunctions solving H|ψ>=0 are not the usual probability amplitudes; they require a Newton-Wigner/Klein-Gordon interpretation.
“The main consequence of (4.12) is to show that, in contrast to the suggestions of [33,34] the wavefunctions q ⊥ , q, q c |ψ which solve the 'Wheeler-DeWitt equation' q ⊥ , q, q c |H |ψ = 0 do not correspond to the usual probability amplitudes, but must instead be interpreted using constructions like those associated with the Newton-Wigner operators and the Klein-Gordon inner product.”
From Almost ideal clocks in quantum cosmology: a brief derivation of time (1995) · cites this paper as [33]
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Quantum effects in a homogeneous dust cloud collapse
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A numerical solution of Schrödinger equation for the dynamics of early universe
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Analyzing quantum gravity spillover in the semiclassical regime
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Birth of an Isotropic and Homogeneous Universe with a Running Cosmological Constant
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- Authors
- Gotay, M. J., & Demaret, J.
- Affiliations
- University of Calgary (CA)
- University of Liège (BE)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1983-11-15
- Volume
- 28
- Issue
- 10
- Pages
- 2402-2413
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W2009198547
- Cited by
- 107
- References
- 20
- Citations by year
- 2026: 4 · 2025: 5 · 2024: 4 · 2023: 5 · 2022: 4 · 2021: 4 · 2020: 2 · 2019: 1 · 2018: 2 · 2017: 3 · 2016: 2 · 2015: 3 · 2014: 1 · 2013: 2
- FWCI
- 0.76
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- quantum cosmology, spacetime singularities, wave function collapse, unitarity, time gauge, cosmic time, geometric time, FRW universe, dust cosmology, singularity avoidance, boundary conditions
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