Smooth quantum dynamics of the mixmaster universe

Bergeron, Hervé; Czuchry, Ewa; Gazeau, Jean‐Pierre; Małkiewicz, Przemysław; Piechocki, Włodzimierz

doi:10.1103/physrevd.92.061302

Cited by 32 publications

(58 citation statements)

References 27 publications

(26 reference statements)

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“…Our fully quantum results show that the preliminary results obtained for the diagonal BIX within the semiclassical affine coherent states approximation [29,30] are correct. Appendix B presents the affine coherent states applied in these papers, which define another parametrization of our coherent states.…”

Section: Discussionsupporting

confidence: 67%

Quantum Belinski–Khalatnikov–Lifshitz scenario

Piechocki

Plewa

2019

Eur. Phys. J. C

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We present the quantum model of the asymptotic dynamics underlying the Belinski-Khalatnikov-Lifshitz (BKL) scenario. The symmetry of the physical phase space enables making use of the affine coherent states quantization. Our results show that quantum dynamics is regular in the sense that during quantum evolution the expectation values of all considered observables are finite. The classical singularity of the BKL scenario is replaced by the quantum bounce that presents a unitary evolution of considered gravitational system. Our results suggest that quantum general relativity has a good chance to be free from singularities.

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Section: Discussionsupporting

confidence: 67%

Quantum Belinski–Khalatnikov–Lifshitz scenario

Piechocki

Plewa

2019

Eur. Phys. J. C

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“…This work is a continuation of previous studies devoted to affine integral quantization of the half-plane [1,2,3,4] and its applications to early or quantum cosmology [5,6,7,8,9,10]. In the latter works, the method was based on the use of affine coherent states or wavelets.…”

Section: Introductionmentioning

confidence: 93%

Covariant affine integral quantization(s)

Gazeau

Murenzi

2016

Journal of Mathematical Physics

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Abstract. Covariant affine integral quantization of the half-plane is studied and applied to the motion of a particle on the half-line. We examine the consequences of different quantizer operators built from weight functions on the half-plane. To illustrate the procedure, we examine two particular choices of the weight function, yielding thermal density operators and affine inversion respectively. The former gives rise to a temperature-dependent probability distribution on the half-plane whereas the later yields the usual canonical quantization and a quasi-probability distribution (affine Wigner function) which is real, marginal in both momentum p and position q.

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“…A straightforward quantization of this Hamiltonian would be given in terms of the dilation generatorD = V H, which is well-defined and self-adjoint in a quantization of the positive real line, V > 0. It is therefore a basic operator in affine quantum cosmology [40,41,42,43,44], in which the volume is restricted to positive values. In loop quantum cosmology, both signs are allowed for the oriented volume v, taking into account the orientation of space.…”

Section: Loop Quantum Cosmology As a Discrete Affine Theorymentioning

confidence: 99%

Critical Evaluation of Common Claims in Loop Quantum Cosmology

Bojowald

2020

Universe

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A large number of models have been analyzed in loop quantum cosmology, using mainly minisuperspace constructions and perturbations. At the same time, general physics principles from effective field theory and covariance have often been ignored. A consistent introduction of these ingredients requires substantial modifications of existing scenarios. As a consequence, none of the broader claims made mainly by the Ashtekar school -such as the genericness of bounces with astonishingly semiclassical dynamics, robustness with respect to quantization ambiguities, the realization of covariance, and the relevance of certain technical results for potential observations -hold up to scrutiny. Several useful lessons for a sustainable version of quantum cosmology can be drawn from this outcome. * e-mail address: bojowald@gravity.psu.edu 1 All quotations from [1] given in this paper refer to the second preprint version.

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Smooth quantum dynamics of the mixmaster universe

Cited by 32 publications

References 27 publications

Quantum Belinski–Khalatnikov–Lifshitz scenario

Quantum Belinski–Khalatnikov–Lifshitz scenario

Covariant affine integral quantization(s)

Critical Evaluation of Common Claims in Loop Quantum Cosmology

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