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3 pages, 3039 KiB

Open AccessEditorial

Editorial to the Special Issue “Quantum Cosmology”

by Paulo Vargas Moniz

Universe 2022, 8(6), 336; https://doi.org/10.3390/universe8060336 - 20 Jun 2022

Cited by 1 | Viewed by 1286

Abstract

Some time ago, when I first inquired as to ‘what quantum cosmology is about’, I did approach the hall with a combination of caution as well as eagerness [...] Full article

(This article belongs to the Special Issue Quantum Cosmology)

Research

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18 pages, 362 KiB

Open AccessEditor’s ChoiceArticle

Minisuperspace Quantum Cosmology in Metric and Affine Theories of Gravity

by Salvatore Capozziello and Francesco Bajardi

Universe 2022, 8(3), 177; https://doi.org/10.3390/universe8030177 - 10 Mar 2022

Cited by 11 | Viewed by 2632

Abstract

Minisuperspace Quantum Cosmology is an approach by which it is possible to infer initial conditions for dynamical systems which can suitably represent observable and non-observable universes. Here we discuss theories of gravity which, from various points of view, extend Einstein’s General Relativity. Specifically, [...] Read more.

Minisuperspace Quantum Cosmology is an approach by which it is possible to infer initial conditions for dynamical systems which can suitably represent observable and non-observable universes. Here we discuss theories of gravity which, from various points of view, extend Einstein’s General Relativity. Specifically, the Hamiltonian formalism for

f (R)

,

f (T)

, and

f (G)

gravity, with R, T, and

G

being the curvature, torsion and Gauss–Bonnet scalars, respectively, is developed starting from the Arnowitt–Deser–Misner approach. The Minisuperspace Quantum Cosmology is derived for all these models and cosmological solutions are obtained thanks to the existence of Noether symmetries. The Hartle criterion allows the interpretation of solutions in view of observable universes. Full article

(This article belongs to the Special Issue Quantum Cosmology)

12 pages, 729 KiB

Open AccessArticle

Clocks and Trajectories in Quantum Cosmology

by Przemysław Małkiewicz, Patrick Peter and Sandro Dias Pinto Vitenti

Universe 2022, 8(2), 71; https://doi.org/10.3390/universe8020071 - 26 Jan 2022

Cited by 5 | Viewed by 1940

Abstract

We consider a simple cosmological model consisting of an empty Bianchi I Universe, whose Hamiltonian we deparametrise to provide a natural clock variable. The model thus effectively describes an isotropic universe with an induced clock given by the shear. By quantising this model, [...] Read more.

We consider a simple cosmological model consisting of an empty Bianchi I Universe, whose Hamiltonian we deparametrise to provide a natural clock variable. The model thus effectively describes an isotropic universe with an induced clock given by the shear. By quantising this model, we obtain various different possible bouncing trajectories (semiquantum expectation values on coherent states or obtained by the de Broglie–Bohm formulation) and explicit their clock dependence, specifically emphasising the question of symmetry across the bounce. Full article

(This article belongs to the Special Issue Quantum Cosmology)

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15 pages, 735 KiB

Open AccessArticle

Topics in Supersymmetric and Noncommutative Quantum Cosmology

by Hugo García-Compeán, Octavio Obregón and Cupatitzio Ramírez

Universe 2021, 7(11), 434; https://doi.org/10.3390/universe7110434 - 12 Nov 2021

Cited by 8 | Viewed by 1840

Abstract

In the present article we review the work carried out by us and collaborators on supersymmetric quantum cosmology, noncommutative quantum cosmology and the application of GUPs to quantum cosmology and black holes. The review represents our personal view on these subjects and it [...] Read more.

In the present article we review the work carried out by us and collaborators on supersymmetric quantum cosmology, noncommutative quantum cosmology and the application of GUPs to quantum cosmology and black holes. The review represents our personal view on these subjects and it is presented in chronological order. Full article

(This article belongs to the Special Issue Quantum Cosmology)

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10 pages, 255 KiB

Open AccessArticle

Cosmic Tangle: Loop Quantum Cosmology and CMB Anomalies

by Martin Bojowald

Universe 2021, 7(6), 186; https://doi.org/10.3390/universe7060186 - 6 Jun 2021

Cited by 5 | Viewed by 1724

Abstract

Loop quantum cosmology is a conflicted field in which exuberant claims of observability coexist with serious objections against the conceptual and physical viability of its current formulations. This contribution presents a non-technical case study of the recent claim that loop quantum cosmology might [...] Read more.

Loop quantum cosmology is a conflicted field in which exuberant claims of observability coexist with serious objections against the conceptual and physical viability of its current formulations. This contribution presents a non-technical case study of the recent claim that loop quantum cosmology might alleviate anomalies in the observations of the cosmic microwave background. Full article

(This article belongs to the Special Issue Quantum Cosmology)

Review

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20 pages, 1950 KiB

Open AccessReview

Shape Invariant Potentials in Supersymmetric Quantum Cosmology

by Shahram Jalalzadeh, Seyed Meraj M. Rasouli and Paulo Moniz

Universe 2022, 8(6), 316; https://doi.org/10.3390/universe8060316 - 5 Jun 2022

Cited by 6 | Viewed by 2254

Abstract

In this brief review, we comment on the concept of shape invariant potentials, which is an essential feature in many settings of

N = 2

supersymmetric quantum mechanics. To motivate its application within supersymmetric quantum cosmology, we present a case study to illustrate [...] Read more.

In this brief review, we comment on the concept of shape invariant potentials, which is an essential feature in many settings of

N = 2

supersymmetric quantum mechanics. To motivate its application within supersymmetric quantum cosmology, we present a case study to illustrate the value of this promising tool. Concretely, we take a spatially flat FRW model in the presence of a single scalar field, minimally coupled to gravity. Then, we extract the associated Schrödinger–Wheeler–DeWitt equation, allowing for a particular scope of factor ordering. Subsequently, we compute the corresponding supersymmetric partner Hamiltonians,

H_{1}

and

H_{2}

. Moreover, we point out how the shape invariance property can be employed to bring a relation among several factor orderings choices for our Schrödinger–Wheeler–DeWitt equation. The ground state is retrieved, and the excited states easily written. Finally, the Hamiltonians,

H_{1}

and

H_{2}

, are explicitly presented within a

N = 2

supersymmetric quantum mechanics framework. Full article

(This article belongs to the Special Issue Quantum Cosmology)

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28 pages, 451 KiB

Open AccessReview

Weyl Curvature Hypothesis in Light of Quantum Backreaction at Cosmological Singularities or Bounces

by Bei-Lok Hu

Universe 2021, 7(11), 424; https://doi.org/10.3390/universe7110424 - 7 Nov 2021

Cited by 6 | Viewed by 1940

Abstract

The Weyl curvature constitutes the radiative sector of the Riemann curvature tensor and gives a measure of the anisotropy and inhomogeneities of spacetime. Penrose’s 1979 Weyl curvature hypothesis (WCH) assumes that the universe began at a very low gravitational entropy state, corresponding to [...] Read more.

The Weyl curvature constitutes the radiative sector of the Riemann curvature tensor and gives a measure of the anisotropy and inhomogeneities of spacetime. Penrose’s 1979 Weyl curvature hypothesis (WCH) assumes that the universe began at a very low gravitational entropy state, corresponding to zero Weyl curvature, namely, the Friedmann–Lemaître–Robertson–Walker (FLRW) universe. This is a simple assumption with far-reaching implications. In classical general relativity, Belinsky, Khalatnikov and Lifshitz (BKL) showed in the 70s that the most general cosmological solutions of the Einstein equation are that of the inhomogeneous Kasner types, with intermittent alteration of the one direction of contraction (in the cosmological expansion phase), according to the mixmaster dynamics of Misner (M). How could WCH and BKL-M co-exist? An answer was provided in the 80s with the consideration of quantum field processes such as vacuum particle creation, which was copious at the Planck time (

10^{- 43}

s), and their backreaction effects were shown to be so powerful as to rapidly damp away the irregularities in the geometry. It was proposed that the vaccum viscosity due to particle creation can act as an efficient transducer of gravitational entropy (large for BKL-M) to matter entropy, keeping the universe at that very early time in a state commensurate with the WCH. In this essay I expand the scope of that inquiry to a broader range, asking how the WCH would fare with various cosmological theories, from classical to semiclassical to quantum, focusing on their predictions near the cosmological singularities (past and future) or avoidance thereof, allowing the Universe to encounter different scenarios, such as undergoing a phase transition or a bounce. WCH is of special importance to cyclic cosmologies, because any slight irregularity toward the end of one cycle will generate greater anisotropy and inhomogeneities in the next cycle. We point out that regardless of what other processes may be present near the beginning and the end states of the universe, the backreaction effects of quantum field processes probably serve as the best guarantor of WCH because these vacuum processes are ubiquitous, powerful and efficient in dissipating the irregularities to effectively nudge the Universe to a near-zero Weyl curvature condition. Full article

(This article belongs to the Special Issue Quantum Cosmology)

62 pages, 2049 KiB

Open AccessReview

Quantum Cosmology with Third Quantisation

by Salvador J. Robles-Pérez

Universe 2021, 7(11), 404; https://doi.org/10.3390/universe7110404 - 27 Oct 2021

Cited by 8 | Viewed by 2152

Abstract

We reviewed the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analysed the information contained in the solutions of the Wheeler–DeWitt equation and showed their interpretation in terms [...] Read more.

We reviewed the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analysed the information contained in the solutions of the Wheeler–DeWitt equation and showed their interpretation in terms of the customary boundary conditions that are typically imposed on the semiclassical wave functions. In particular, we reviewed three different paradigms for the quantum creation of a homogeneous and isotropic universe. For the quantisation of a non-simply connected manifold, the best framework is the third quantisation formalism, in which the wave function of the universe is seen as a field that propagates in the space of Riemannian 3-geometries, which turns out to be isomorphic to a (part of a) 1 + 5 Minkowski spacetime. Thus, the quantisation of the wave function follows the customary formalism of a quantum field theory. A general review of the formalism is given, and the creation of the universes is analysed, including their initial expansion and the appearance of matter after inflation. These features are presented in more detail in the case of a homogeneous and isotropic universe. The main conclusion in both cases is that the most natural way in which the universes should be created is in entangled universe–antiuniverse pairs. Full article

(This article belongs to the Special Issue Quantum Cosmology)

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20 pages, 3594 KiB

Open AccessReview

Fuzzy Instantons in Landscape and Swampland: Review of the Hartle–Hawking Wave Function and Several Applications

by Dong-han Yeom

Universe 2021, 7(10), 367; https://doi.org/10.3390/universe7100367 - 30 Sep 2021

Cited by 4 | Viewed by 2016

Abstract

The Euclidean path integral is well approximated by instantons. If instantons are dynamical, they will necessarily be complexified. Fuzzy instantons can have multiple physical applications. In slow-roll inflation models, fuzzy instantons can explain the probability distribution of the initial conditions of the universe. [...] Read more.

The Euclidean path integral is well approximated by instantons. If instantons are dynamical, they will necessarily be complexified. Fuzzy instantons can have multiple physical applications. In slow-roll inflation models, fuzzy instantons can explain the probability distribution of the initial conditions of the universe. Although the potential shape does not satisfy the slow-roll conditions due to the swampland criteria, the fuzzy instantons can still explain the origin of the universe. If we extend the Euclidean path integral beyond the Hartle–Hawking no-boundary proposal, it becomes possible to examine fuzzy Euclidean wormholes that have multiple physical applications in cosmology and black hole physics. Full article

(This article belongs to the Special Issue Quantum Cosmology)

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55 pages, 1422 KiB

Open AccessReview

An Overview on the Nature of the Bounce in LQC and PQM

by Gabriele Barca, Eleonora Giovannetti and Giovanni Montani

Universe 2021, 7(9), 327; https://doi.org/10.3390/universe7090327 - 1 Sep 2021

Cited by 31 | Viewed by 2537

Abstract

We present a review on some of the basic aspects concerning quantum cosmology in the presence of cut-off physics as it has emerged in the literature during the last fifteen years. We first analyze how the Wheeler–DeWitt equation describes the quantum Universe dynamics, [...] Read more.

We present a review on some of the basic aspects concerning quantum cosmology in the presence of cut-off physics as it has emerged in the literature during the last fifteen years. We first analyze how the Wheeler–DeWitt equation describes the quantum Universe dynamics, when a pure metric approach is concerned, showing how, in general, the primordial singularity is not removed by the quantum effects. We then analyze the main implications of applying the loop quantum gravity prescriptions to the minisuperspace model, i.e., we discuss the basic features of the so-called loop quantum cosmology. For the isotropic Universe dynamics, we compare the original approach, dubbed the

μ_{0}

scheme, and the most commonly accepted formulation for which the area gap is taken as physically scaled, i.e., the so-called

\bar{μ}

scheme. Furthermore, some fundamental results concerning the Bianchi Universes are discussed, especially with respect to the morphology of the Bianchi IX model. Finally, we consider some relevant criticisms developed over the last ten years about the real link existing between the full theory of loop quantum gravity and its minisuperspace implementation, especially with respect to the preservation of the internal

S U (2)

symmetry. In the second part of the review, we consider the dynamics of the isotropic Universe and of the Bianchi models in the framework of polymer quantum mechanics. Throughout the paper, we focus on the effective semiclassical dynamics and study the full quantum theory only in some cases, such as the FLRW model and the Bianchi I model in the Ashtekar variables. We first address the polymerization in terms of the Ashtekar–Barbero–Immirzi connection and show how the resulting dynamics is isomorphic to the

μ_{0}

scheme of loop quantum cosmology with a critical energy density of the Universe that depends on the initial conditions of the dynamics. The following step is to analyze the polymerization of volume-like variables, both for the isotropic and Bianchi I models, and we see that if the Universe volume (the cubed scale factor) is one of the configurational variables, then the resulting dynamics is isomorphic to that one emerging in loop quantum cosmology for the

\bar{μ}

scheme, with the critical energy density value being fixed only by fundamental constants and the Immirzi parameter. Finally, we consider the polymer quantum dynamics of the homogeneous and inhomogeneous Mixmaster model by means of a metric approach. In particular, we compare the results obtained by using the volume variable, which leads to the emergence of a singularity- and chaos-free cosmology, to the use of the standard Misner variable. In the latter case, we deal with the surprising result of a cosmology that is still singular, and its chaotic properties depend on the ratio between the lattice steps for the isotropic and anisotropic variables. We conclude the review with some considerations of the problem of changing variables in the polymer representation of the minisuperspace dynamics. In particular, on a semiclassical level, we consider how the dynamics can be properly mapped in two different sets of variables (at the price of having to deal with a coordinate dependent lattice step), and we infer some possible implications on the equivalence of the

μ_{0}

and

\bar{μ}

scheme of loop quantum cosmology. Full article

(This article belongs to the Special Issue Quantum Cosmology)

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20 pages, 351 KiB

Open AccessReview

A Brief Overview of Results about Uniqueness of the Quantization in Cosmology

by Jerónimo Cortez, Guillermo A. Mena Marugán and José M. Velhinho

Universe 2021, 7(8), 299; https://doi.org/10.3390/universe7080299 - 13 Aug 2021

Cited by 4 | Viewed by 1801

Abstract

The purpose of this review is to provide a brief overview of recent conceptual developments regarding possible criteria to guarantee the uniqueness of the quantization in a variety of situations that are found in cosmological systems. These criteria impose certain conditions on the [...] Read more.

The purpose of this review is to provide a brief overview of recent conceptual developments regarding possible criteria to guarantee the uniqueness of the quantization in a variety of situations that are found in cosmological systems. These criteria impose certain conditions on the representation of a group of physically relevant linear transformations. Generally, this group contains any existing symmetry of the spatial sections. These symmetries may or may not be sufficient for the purpose of uniqueness and may have to be complemented with other remaining symmetries that affect the time direction or with dynamical transformations that are, in fact, not symmetries. We discuss the extent to which a unitary implementation of the resulting group suffices to fix the quantization—a demand that can be seen as a weaker version of the requirement of invariance. In particular, a strict invariance under certain transformations may eliminate some physically interesting possibilities in the passage to the quantum theory. This is the first review in which this unified perspective is adopted to discuss otherwise different uniqueness criteria proposed either in homogeneous loop quantum cosmology or in the Fock quantization of inhomogeneous cosmologies. Full article

(This article belongs to the Special Issue Quantum Cosmology)

22 pages, 1641 KiB

Open AccessReview

Hawking Radiation and Black Hole Gravitational Back Reaction—A Quantum Geometrodynamical Simplified Model

by João Marto

Universe 2021, 7(8), 297; https://doi.org/10.3390/universe7080297 - 12 Aug 2021

Cited by 3 | Viewed by 2282

Abstract

The purpose of this paper is to analyse the back reaction problem, between Hawking radiation and the black hole, in a simplified model for the black hole evaporation in the quantum geometrodynamics context. The idea is to transcribe the most important characteristics of [...] Read more.

The purpose of this paper is to analyse the back reaction problem, between Hawking radiation and the black hole, in a simplified model for the black hole evaporation in the quantum geometrodynamics context. The idea is to transcribe the most important characteristics of the Wheeler-DeWitt equation into a Schrödinger’s type of equation. Subsequently, we consider Hawking radiation and black hole quantum states evolution under the influence of a potential that includes back reaction. Finally, entropy is estimated as a measure of the entanglement between the black hole and Hawking radiation states in this model. Full article

(This article belongs to the Special Issue Quantum Cosmology)

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30 pages, 491 KiB

Open AccessReview

Classical and Quantum f(R) Cosmology: The Big Rip, the Little Rip and the Little Sibling of the Big Rip

by Teodor Borislavov Vasilev, Mariam Bouhmadi-López and Prado Martín-Moruno

Universe 2021, 7(8), 288; https://doi.org/10.3390/universe7080288 - 6 Aug 2021

Cited by 9 | Viewed by 2312

Abstract

The big rip, the little rip and the little sibling of the big rip are cosmological doomsdays predicted by some phantom dark-energy models that could describe the future evolution of our universe. When the universe evolves towards either of these future cosmic events, [...] Read more.

The big rip, the little rip and the little sibling of the big rip are cosmological doomsdays predicted by some phantom dark-energy models that could describe the future evolution of our universe. When the universe evolves towards either of these future cosmic events, all bounded structures and, ultimately, space–time itself are ripped apart. Nevertheless, it is commonly believed that quantum gravity effects may smooth or even avoid these classically predicted singularities. In this review, we discuss the classical and quantum occurrence of these riplike events in the scheme of metric

f (R)

theories of gravity. The quantum analysis is performed in the framework of

f (R)

quantum geometrodynamics. In this context, we analyze the fulfilment of the DeWitt criterion for the avoidance of these singular fates. This review contains as well new unpublished work (the analysis of the equation of state for the phantom fluid and a new quantum treatment of the big rip and the little sibling of the big rip events). Full article

(This article belongs to the Special Issue Quantum Cosmology)

17 pages, 358 KiB

Open AccessReview

Quantum and Classical Cosmology in the Brans–Dicke Theory

by Carla R. Almeida, Olesya Galkina and Julio César Fabris

Universe 2021, 7(8), 286; https://doi.org/10.3390/universe7080286 - 5 Aug 2021

Cited by 6 | Viewed by 2020

Abstract

In this paper, we discuss classical and quantum aspects of cosmological models in the Brans–Dicke theory. First, we review cosmological bounce solutions in the Brans–Dicke theory that obeys energy conditions (without ghost) for a universe filled with radiative fluid. Then, we quantize this [...] Read more.

In this paper, we discuss classical and quantum aspects of cosmological models in the Brans–Dicke theory. First, we review cosmological bounce solutions in the Brans–Dicke theory that obeys energy conditions (without ghost) for a universe filled with radiative fluid. Then, we quantize this classical model in a canonical way, establishing the corresponding Wheeler–DeWitt equation in the minisuperspace, and analyze the quantum solutions. When the energy conditions are violated, corresponding to the case

ω < - \frac{3}{2}

, the energy is bounded from below and singularity-free solutions are found. However, in the case

ω > - \frac{3}{2}

, we cannot compute the evolution of the scale factor by evaluating the expectation values because the wave function is not finite (energy spectrum is not bounded from below). However, we can analyze this case using Bohmian mechanics and the de Broglie–Bohm interpretation of quantum mechanics. Using this approach, the classical and quantum results can be compared for any value of

ω

. Full article

(This article belongs to the Special Issue Quantum Cosmology)

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16 pages, 836 KiB

Open AccessReview

Cosmological Particle Production in Quantum Gravity

by Yaser Tavakoli

Universe 2021, 7(8), 258; https://doi.org/10.3390/universe7080258 - 22 Jul 2021

Cited by 2 | Viewed by 1494

Abstract

Quantum theory of a test field on a quantum cosmological spacetime may be viewed as a theory of the test field on an emergent classical background. In such a case, the resulting dressed metric for the field propagation is a function of the [...] Read more.

Quantum theory of a test field on a quantum cosmological spacetime may be viewed as a theory of the test field on an emergent classical background. In such a case, the resulting dressed metric for the field propagation is a function of the quantum fluctuations of the original geometry. When the backreaction is negligible, massive modes can experience an anisotropic Bianchi type I background. The field modes propagating on such a quantum-gravity-induced spacetime can then unveil interesting phenomenological consequences of the super-Planckian scales, such as gravitational particle production. The aim of this paper is to address the issue of gravitational particle production associated with the massive modes in such an anisotropic dressed spacetime. By imposing a suitable adiabatic condition on the vacuum state and computing the energy density of the created particles, the significance of the particle production on the dynamics of the universe in Planck era is discussed. Full article

(This article belongs to the Special Issue Quantum Cosmology)

23 pages, 367 KiB

Open AccessReview

Time and Evolution in Quantum and Classical Cosmology

by Alexander Yu Kamenshchik, Jeinny Nallely Pérez Rodríguez and Tereza Vardanyan

Universe 2021, 7(7), 219; https://doi.org/10.3390/universe7070219 - 30 Jun 2021

Cited by 1 | Viewed by 1736

Abstract

We analyze the issue of dynamical evolution and time in quantum cosmology. We emphasize the problem of choice of phase space variables that can play the role of a time parameter in such a way that for expectation values of quantum operators the [...] Read more.

We analyze the issue of dynamical evolution and time in quantum cosmology. We emphasize the problem of choice of phase space variables that can play the role of a time parameter in such a way that for expectation values of quantum operators the classical evolution is reproduced. We show that it is neither necessary nor sufficient for the Poisson bracket between the time variable and the super-Hamiltonian to be equal to unity in all of the phase space. We also discuss the question of switching between different internal times as well as the Montevideo interpretation of quantum theory. Full article

(This article belongs to the Special Issue Quantum Cosmology)

14 pages, 539 KiB

Open AccessReview

Quantum String Cosmology

by Maurizio Gasperini

Universe 2021, 7(1), 14; https://doi.org/10.3390/universe7010014 - 12 Jan 2021

Cited by 10 | Viewed by 3028

Abstract

We present a short review of possible applications of the Wheeler-De Witt equation to cosmological models based on the low-energy string effective action, and characterised by an initial regime of asymptotically flat, low energy, weak coupling evolution. Considering in particular a class of [...] Read more.

We present a short review of possible applications of the Wheeler-De Witt equation to cosmological models based on the low-energy string effective action, and characterised by an initial regime of asymptotically flat, low energy, weak coupling evolution. Considering in particular a class of duality-related (but classically disconnected) background solutions, we shall discuss the possibility of quantum transitions between the phases of pre-big bang and post-big bang evolution. We will show that it is possible, in such a context, to represent the birth of our Universe as a quantum process of tunneling or “anti-tunneling” from an initial state asymptotically approaching the string perturbative vacuum. Full article

(This article belongs to the Special Issue Quantum Cosmology)

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