Special Issue "Quantum Models for Cosmology"

A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "Cosmology".

Deadline for manuscript submissions: closed (15 February 2022) | Viewed by 7602

Special Issue Editors

Prof. Dr. Jean-Pierre Gazeau
E-Mail Website
Guest Editor
Université Paris Diderot, Sorbonne Paris Cité, 75205 Paris CEDEX 13, France
Interests: (covariant) integral quantization, specially with POVM and coherent states; covariant integral quantization of cosmological models; foundations of quantum physics; deformation of standard probability distributions and related entropies; quantum field theory in de Sitter and Anti-de Sitter space-times, cosmological implications
Special Issues, Collections and Topics in MDPI journals
Dr. Przemyslaw Malkiewicz
E-Mail Website
Guest Editor
National Centre for Nuclear Research, 00-681 Warszawa, Poland
Interests: Classical and quantum gravity; Hamiltonian constraint systems; problem of time; cosmological perturbation theory; quantum bounce models; applications of coherent states in quantum cosmology

Special Issue Information

Dear Colleagues,

The Special Issue is aimed at collecting contributions on all aspects of quantum cosmology, including singularity resolutions, problem of time, semiclassical descriptions, methods of quantization of cosmological models, and quantum cosmological alternatives to inflationary models.

The existing data and available models point to the ΛCDM model of expanding universe starting at the big bang singularity 13.7 billion years ago in a nearly homogeneous, state with tiny and Gaussian matter inhomogeneities over superhorizon scales. Nevertheless, it is commonly accepted that general relativity (and hence ΛCDM) breaks down near the singularity. Thus, we need a better theory that can at once resolve the singularity problem and explain the peculiar primordial universe that has started the present cosmological expansion. It is worth noting that future experiments that aim at detecting and measuring primordial gravitational waves may soon further constrain the primordial state of the Universe.

We wish to invite both original and review papers to this Special Issue, which particularly emphasize ideas and problems of frameworks based on background independent quantum cosmology. We believe that such frameworks have a potential to explain the initial conditions as well as the origin of the expansion in the Universe without inevitably postulating fine-tuned primordial fields. We are interested in collecting contributions on a broad range of approaches and ideas which emphasize the quantum nature of the primordial universe and related issues, like time problem in quantum gravity.

Prof. Dr. Jean-Pierre Gazeau
Dr. Przemyslaw Malkiewicz
Guest Editors

Manuscript Submission Information

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Keywords

  • quantum cosmology
  • singularity resolutions
  • problem of time
  • semiclassical descriptions
  • quantization methods
  • alternatives to inflationary models

Published Papers (7 papers)

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Research

Article
Quantum Capacity and Vacuum Compressibility of Spacetime: Thermal Fields
Universe 2022, 8(5), 291; https://doi.org/10.3390/universe8050291 - 21 May 2022
Viewed by 477
Abstract
An important yet perplexing result from work in the 1990s and 2000s is the near-unity value of the ratio of fluctuations in the vacuum energy density of quantum fields to the mean in a collection of generic spacetimes. This was carried out by [...] Read more.
An important yet perplexing result from work in the 1990s and 2000s is the near-unity value of the ratio of fluctuations in the vacuum energy density of quantum fields to the mean in a collection of generic spacetimes. This was carried out by way of calculating the noise kernels which are the correlators of the stress-energy tensor of quantum fields. In this paper, we revisit this issue via a quantum thermodynamics approach, by calculating two quintessential thermodynamic quantities: the heat capacity and the quantum compressibility of some model geometries filled with a quantum field at high and low temperatures. This is because heat capacity at constant volume gives a measure of the fluctuations of the energy density to the mean. When this ratio approaches or exceeds unity, the validity of the canonical distribution is called into question. Likewise, a system’s compressibility at constant pressure is a criterion for the validity of grand canonical ensemble. We derive the free energy density and, from it, obtain the expressions for these two thermodynamic quantities for thermal and quantum fields in 2d Casimir space, 2d Einstein cylinder and 4d (S1×S3 ) Einstein universe. To examine the dependence on the dimensionality of space, for completeness, we have also derived these thermodynamic quantities for the Einstein universes with even-spatial dimensions: S1×S2 and S1×S4. With this array of spacetimes we can investigate the thermodynamic stability of quantum matter fields in them and make some qualitative observations on the compatibility condition for the co-existence between quantum fields and spacetimes, a fundamental issue in the quantum and gravitation conundrum. Full article
(This article belongs to the Special Issue Quantum Models for Cosmology)
Article
Time in Quantum Cosmology
Universe 2022, 8(1), 36; https://doi.org/10.3390/universe8010036 - 08 Jan 2022
Cited by 2 | Viewed by 401
Abstract
Time in quantum gravity is not a well-defined notion despite its central role in the very definition of dynamics. Using the formalism of quantum geometrodynamics, we briefly review the problem and illustrate it with two proposed solutions. Our main application is quantum cosmology—the [...] Read more.
Time in quantum gravity is not a well-defined notion despite its central role in the very definition of dynamics. Using the formalism of quantum geometrodynamics, we briefly review the problem and illustrate it with two proposed solutions. Our main application is quantum cosmology—the application of quantum gravity to the Universe as a whole. Full article
(This article belongs to the Special Issue Quantum Models for Cosmology)
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Communication
Effect of Fast Scale Factor Fluctuations on Cosmological Evolution
Universe 2021, 7(6), 164; https://doi.org/10.3390/universe7060164 - 27 May 2021
Viewed by 757
Abstract
In this paper, we study the corrections to the Friedmann equations due to fast fluctuations in the universe scale factor. Such fast quantum fluctuations were recently proposed as a potential solution to the cosmological constant problem. They also induce strong changes to the [...] Read more.
In this paper, we study the corrections to the Friedmann equations due to fast fluctuations in the universe scale factor. Such fast quantum fluctuations were recently proposed as a potential solution to the cosmological constant problem. They also induce strong changes to the current sign and magnitude of the average cosmological force, thus making them one of the potential probable causes of the modification of Newtonian dynamics in galaxy-scale systems. It appears that quantum fluctuations in the scale factor also modify the Friedmann equations, leading to a considerable modification of cosmological evolution. In particular, they give rise to the late-time accelerated expansion of the universe, and they may also considerably modify the effective universe potential. Full article
(This article belongs to the Special Issue Quantum Models for Cosmology)
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Article
Revisiting the Cosmological Constant Problem within Quantum Cosmology
Universe 2020, 6(8), 108; https://doi.org/10.3390/universe6080108 - 02 Aug 2020
Cited by 6 | Viewed by 1749
Abstract
A new perspective on the Cosmological Constant Problem (CCP) is proposed and discussed within the multiverse approach of Quantum Cosmology. It is assumed that each member of the ensemble of universes has a characteristic scale a that can be used as integration variable [...] Read more.
A new perspective on the Cosmological Constant Problem (CCP) is proposed and discussed within the multiverse approach of Quantum Cosmology. It is assumed that each member of the ensemble of universes has a characteristic scale a that can be used as integration variable in the partition function. An averaged characteristic scale of the ensemble is estimated by using only members that satisfy the Einstein field equations. The averaged characteristic scale is compatible with the Planck length when considering an ensemble of solutions to the Einstein field equations with an effective cosmological constant. The multiverse ensemble is split in Planck-seed universes with vacuum energy density of order one; thus, Λ˜8π in Planck units and a-derivable universes. For a-derivable universe with a characteristic scale of the order of the observed Universe a8×1060, the cosmological constant Λ=Λ˜/a2 is in the range 1012110122, which is close in magnitude to the observed value 10123. We point out that the smallness of Λ can be viewed to be natural if its value is associated with the entropy of the Universe. This approach to the CCP reconciles the Planck-scale huge vacuum energy–density predicted by QFT considerations, as valid for Planck-seed universes, with the observed small value of the cosmological constant as relevant to an a-derivable universe as observed. Full article
(This article belongs to the Special Issue Quantum Models for Cosmology)
Article
Quantum Cosmology of Fab Four John Theory with Conformable Fractional Derivative
Universe 2020, 6(4), 50; https://doi.org/10.3390/universe6040050 - 31 Mar 2020
Cited by 4 | Viewed by 1088
Abstract
We study a quantization via fractional derivative of a nonminimal derivative coupling cosmological theory, namely, the Fab Four John theory. Its Hamiltonian version presents the issue of fractional powers in the momenta. That problem is solved here by the application of the so-called [...] Read more.
We study a quantization via fractional derivative of a nonminimal derivative coupling cosmological theory, namely, the Fab Four John theory. Its Hamiltonian version presents the issue of fractional powers in the momenta. That problem is solved here by the application of the so-called conformable fractional derivative. This leads to a Wheeler–DeWitt equation of second order, showing that a Bohm–de Broglie interpretation can be constructed. That combination of fractional quantization and Bohmian interpretation provides us a new quantization method, in which the quantum potential is the criterion to say if a quantum solution is acceptable or not to be further studied. We show that a wide range of solutions for the scale factor is possible. Among all of those, a bouncing solution analogous to the perfect fluid cosmology seems to deserve special attention. Full article
(This article belongs to the Special Issue Quantum Models for Cosmology)
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Article
Critical Evaluation of Common Claims in Loop Quantum Cosmology
Universe 2020, 6(3), 36; https://doi.org/10.3390/universe6030036 - 26 Feb 2020
Cited by 33 | Viewed by 1394
Abstract
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 [...] Read more.
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 evaluation. Full article
(This article belongs to the Special Issue Quantum Models for Cosmology)
Article
Quantum Mixmaster as a Model of the Primordial Universe
Universe 2020, 6(1), 7; https://doi.org/10.3390/universe6010007 - 31 Dec 2019
Cited by 12 | Viewed by 1067
Abstract
The Mixmaster solution to Einstein field equations was examined by C. Misner in an effort to better understand the dynamics of the early universe. We highlight the importance of the quantum version of this model for the early universe. This quantum version and [...] Read more.
The Mixmaster solution to Einstein field equations was examined by C. Misner in an effort to better understand the dynamics of the early universe. We highlight the importance of the quantum version of this model for the early universe. This quantum version and its semi-classical portraits are yielded through affine and standard coherent state quantizations and more generally affine and Weyl–Heisenberg covariant integral quantizations. The adiabatic and vibronic approximations widely used in molecular physics can be employed to qualitatively study the dynamics of the model on both quantum and semi-classical levels. Moreover, the semi-classical approach with the exact anisotropy potential can be effective in the numerical integration of some solutions. Some promising physical features such as the singularity resolution, smooth bouncing, the excitation of anisotropic oscillations and a substantial amount of post-bounce inflation as the backreaction to the latter are pointed out. Finally, a realistic cosmological scenario based on the quantum mixmaster model, which includes the formation and evolution of local structures is outlined. Full article
(This article belongs to the Special Issue Quantum Models for Cosmology)
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