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2 pages, 155 KiB

Open AccessEditorial

Quantum Models for Cosmology

by Jean-Pierre Gazeau and Przemysław Małkiewicz

Universe 2022, 8(10), 531; https://doi.org/10.3390/universe8100531 - 13 Oct 2022

Viewed by 1268

Abstract

This Special Issue presents a collection of review and original papers on various aspects and applications of quantum cosmological models [...] Full article

(This article belongs to the Special Issue Quantum Models for Cosmology)

Research

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29 pages, 402 KiB

Open AccessArticle

Quantum Capacity and Vacuum Compressibility of Spacetime: Thermal Fields

by Hing-Tong Cho, Jen-Tsung Hsiang and Bei-Lok Hu

Universe 2022, 8(5), 291; https://doi.org/10.3390/universe8050291 - 21 May 2022

Cited by 6 | Viewed by 2226

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 (

S^{1} \times S^{3}

) 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:

S^{1} \times S^{2}

and

S^{1} \times S^{4}

. 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)

16 pages, 1357 KiB

Open AccessArticle

Time in Quantum Cosmology

by Claus Kiefer and Patrick Peter

Universe 2022, 8(1), 36; https://doi.org/10.3390/universe8010036 - 8 Jan 2022

Cited by 25 | Viewed by 2385

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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9 pages, 1033 KiB

Open AccessCommunication

Effect of Fast Scale Factor Fluctuations on Cosmological Evolution

by Igor I. Smolyaninov

Universe 2021, 7(6), 164; https://doi.org/10.3390/universe7060164 - 27 May 2021

Cited by 2 | Viewed by 2187

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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15 pages, 325 KiB

Open AccessEditor’s ChoiceArticle

Revisiting the Cosmological Constant Problem within Quantum Cosmology

by Vesselin G. Gueorguiev and Andre Maeder

Universe 2020, 6(8), 108; https://doi.org/10.3390/universe6080108 - 2 Aug 2020

Cited by 9 | Viewed by 4050

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,

\tilde{Λ} \approx 8 π

in Planck units and a-derivable universes. For a-derivable universe with a characteristic scale of the order of the observed Universe

a \approx 8 \times 10^{60}

, the cosmological constant

Λ = \tilde{Λ} / a^{2}

is in the range

10^{- 121}

–

10^{- 122}

, which is close in magnitude to the observed value

10^{- 123}

. 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)

20 pages, 793 KiB

Open AccessArticle

Quantum Cosmology of Fab Four John Theory with Conformable Fractional Derivative

by Isaac Torres, Júlio César Fabris, Oliver Fabio Piattella and Antônio Brasil Batista

Universe 2020, 6(4), 50; https://doi.org/10.3390/universe6040050 - 31 Mar 2020

Cited by 15 | Viewed by 2849

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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23 pages, 377 KiB

Open AccessArticle

Critical Evaluation of Common Claims in Loop Quantum Cosmology

by Martin Bojowald

Universe 2020, 6(3), 36; https://doi.org/10.3390/universe6030036 - 26 Feb 2020

Cited by 44 | Viewed by 3305

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)

26 pages, 681 KiB

Open AccessArticle

Quantum Mixmaster as a Model of the Primordial Universe

by Hervé Bergeron, Ewa Czuchry, Jean Pierre Gazeau and Przemysław Małkiewicz

Universe 2020, 6(1), 7; https://doi.org/10.3390/universe6010007 - 31 Dec 2019

Cited by 18 | Viewed by 2763

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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