Quantum Cosmology in the Light of Quantum Mechanics

There is a formal analogy between the evolution of the universe, when this is seen as a trajectory in the minisuperspace, and the worldline followed by a test particle in a curved spacetime. The analogy can be extended to the quantum realm, where the trajectories are transformed into wave packets that give us the probability of finding the universe or the particle in a given point of their respective spaces: the spacetime in the case of the particle and the minisuperspace in the case of the universe. The wave function of the spacetime and the matter fields, all together, can then be seen as a super-field that propagates in the minisuperspace and the so-called third quantisation procedure can be applied in a parallel way as the second quantisation procedure is performed with a matter field that propagates in the spacetime. The super-field can thus be interpreted as made up of universes propagating, i.e. evolving, in the minisuperspace. The analogy can also be used in the opposite direction. The way in which the semiclassical state of the universe is obtained in quantum cosmology allows us to obtain, from the quantum state of a field that propagates in the spacetime, the geodesics of the underlying spacetime as well as their quantum uncertainties or dispersions. This might settle a new starting point for a different quantisation of the spacetime.

Quantum Cosmology in the Light of Quantum Mechanics

Galaxies ◽

10.3390/galaxies7020050 ◽

2019 ◽

Vol 7 (2) ◽

pp. 50

Author(s):

Salvador J. Robles-Pérez

Keyword(s):

Wave Function ◽

Quantum Mechanics ◽

Quantum State ◽

Test Particle ◽

Quantum Cosmology ◽

Matter Field ◽

Starting Point ◽

The Universe ◽

Semiclassical State ◽

There is a formal analogy between the evolution of the universe, when it is seen as a trajectory in the minisuperspace, and the worldline followed by a test particle in a curved spacetime. The analogy can be extended to the quantum realm, where the trajectories are transformed into wave packets that give us the probability of finding the universe or the particle in a given point of their respective spaces: the spacetime in the case of the particle and the minisuperspace in the case of the universe. The wave function of the spacetime and the matter fields, all together, can then be seen as a super-field that propagates in the minisuperspace and the so-called third quantisation procedure can be applied in a parallel way as the second quantisation procedure is performed with a matter field that propagates in the spacetime. The super-field can thus be interpreted as made up of universes propagating, i.e., evolving, in the minisuperspace. The analogy can also be used in the opposite direction. The way in which the semiclassical state of the universe is obtained in quantum cosmology allows us to obtain, from the quantum state of a field that propagates in the spacetime, the geodesics of the underlying spacetime as well as their quantum uncertainties or dispersions. This might settle a new starting point for a different quantisation of the spacetime.

INTERPRETATION AND PREDICTABILITY OF QUANTUM MECHANICS AND QUANTUM COSMOLOGY

Modern Physics Letters A ◽

10.1142/s0217732388000775 ◽

1988 ◽

Vol 03 (07) ◽

pp. 645-651 ◽

Cited By ~ 7

Author(s):

SUMIO WADA

Keyword(s):

Wave Function ◽

Quantum Mechanics ◽

Quantum Theory ◽

Physical Meaning ◽

Quantum Cosmology ◽

Degrees Of Freedom ◽

Interpretation Of Quantum Mechanics ◽

Probabilistic Interpretation ◽

The Universe ◽

Classical Picture

A non-probabilistic interpretation of quantum mechanics asserts that we get a prediction only when a wave function has a peak. Taking this interpretation seriously, we discuss how to find a peak in the wave function of the universe, by using some minisuperspace models with homogeneous degrees of freedom and also a model with cosmological perturbations. Then we show how to recover our classical picture of the universe from the quantum theory, and comment on the physical meaning of the backreaction equation.

ζ-FUNCTION TECHNIQUE FOR QUANTUM COSMOLOGY: THE CONTRIBUTIONS OF MATTER FIELDS TO THE HARTLE-HAWKING WAVE FUNCTION OF THE UNIVERSE

International Journal of Modern Physics A ◽

10.1142/s0217751x92001654 ◽

1992 ◽

Vol 07 (16) ◽

pp. 3713-3746 ◽

Cited By ~ 35

Author(s):

A. YU. KAMENSHCHIK ◽

I.V. MISHAKOV

Keyword(s):

Wave Function ◽

Quantum Cosmology ◽

Scaling Behavior ◽

Function Technique ◽

Loop Approximation ◽

The One ◽

The Universe ◽

We investigate the contributions of matter fields to the Hartle-Hawking wave function of the Universe in the one-loop approximation. The values ζ(0), which describe the scaling behavior of the wave function calculated on the background representing the part of four-dimensional DeSitter sphere, are calculated for scalar, electromagnetic, graviton, spin-1/2 and spin-3/2 fields. The ζ-function technique is used and developed for these calculations. The obtained results can be applied to a detailed investigation of the structure of the Hartle-Hawking wave function.

Wave Packet in Quantum Cosmology and Definition of Semiclassical Time

International Journal of Modern Physics A ◽

10.1142/s0217751x97000657 ◽

1997 ◽

Vol 12 (05) ◽

pp. 859-871

Author(s):

Y. Ohkuwa ◽

T. Kitazoe

Keyword(s):

Wave Function ◽

Scalar Field ◽

Wave Packet ◽

Quantum Cosmology ◽

Matter Field ◽

Time Variable ◽

Wave Functions ◽

Quantum Matter ◽

Definition Of ◽

We consider a quantum cosmology with a massless background scalar field ϕB and adopt a wave packet as the wave function. This wave packet is a superposition of the WKB form wave functions, each of which has a definite momentum of the scalar field ϕB. In this model it is shown that to trace the formalism of the WKB time is seriously difficult without introducing a complex value for a time. We define a semiclassical real time variable TP from the phase of the wave packet and calculate it explicitly. We find that, when a quantum matter field ϕQ is coupled to the system, an approximate Schrödinger equation for ϕQ holds with respect to TP in a region where the size a of the universe is large and |ϕB| is small.

p-ADIC AND ADELIC MINISUPERSPACE QUANTUM COSMOLOGY

International Journal of Modern Physics A ◽

10.1142/s0217751x02009734 ◽

2002 ◽

Vol 17 (10) ◽

pp. 1413-1433 ◽

Cited By ~ 16

Author(s):

GORAN S. DJORDJEVIĆ ◽

BRANKO DRAGOVICH ◽

LJUBIŠA D. NEŠIĆ ◽

IGOR V. VOLOVICH

Keyword(s):

Quantum Mechanics ◽

Cosmological Constant ◽

Quantum Cosmology ◽

Quantum Effects ◽

De Sitter Space ◽

Cosmological Models ◽

De Sitter ◽

Adelic Quantum Mechanics ◽

We consider the formulation and some elaboration of p-adic and adelic quantum cosmology. The adelic generalization of the Hartle–Hawking proposal does not work in models with matter fields. p-adic and adelic minisuperspace quantum cosmology is well defined as an ordinary application of p-adic and adelic quantum mechanics. It is illustrated by a few cosmological models in one, two and three minisuperspace dimensions. As a result of p-adic quantum effects and the adelic approach, these models exhibit some discreteness of the minisuperspace and cosmological constant. In particular, discreteness of the de Sitter space and its cosmological constant is emphasized.

1-loop quantum cosmology: the contributions of matter fields to the wavefunction of the universe

Classical and Quantum Gravity ◽

10.1088/0264-9381/9/2/002 ◽

1992 ◽

Vol 9 (2) ◽

pp. L27-L32 ◽

Cited By ~ 23

Author(s):

A O Barvinsky ◽

A Y Kamenshchik ◽

I P Karmazin ◽

I V Mishakov

Keyword(s):

Quantum Cosmology ◽

Loop Quantum Cosmology ◽

The Universe ◽

Quantum cosmology with dynamical vacuum in a minimal-length scenario

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09114-8 ◽

2021 ◽

Vol 81 (4) ◽

Author(s):

M. F. Gusson ◽

A. Oakes O. Gonçalves ◽

R. G. Furtado ◽

J. C. Fabris ◽

J. A. Nogueira

Keyword(s):

Wave Function ◽

Commutation Relation ◽

Uncertainty Principle ◽

Quantum Cosmology ◽

Generalized Uncertainty Principle ◽

Minimal Length ◽

Minimum Length ◽

Position Space ◽

Infinite Norm ◽

AbstractIn this work, we consider effects of the dynamical vacuum in quantum cosmology in presence of a minimum length introduced by the GUP (generalized uncertainty principle) related to the modified commutation relation $$[{\hat{X}},{\hat{P}}] := \frac{i\hbar }{ 1 - \beta {\hat{P}}^2 }$$ [ X ^ , P ^ ] : = i ħ 1 - β P ^ 2 . We determine the wave function of the Universe $$ \psi _{qp}(\xi ,t)$$ ψ qp ( ξ , t ) , which is solution of the modified Wheeler–DeWitt equation in the representation of the quasi-position space, in the limit where the scale factor of the Universe is small. Although $$\psi _{qp}(\xi ,t)$$ ψ qp ( ξ , t ) is a physically acceptable state it is not a realizable state of the Universe because $$ \psi _{qp}(\xi ,t)$$ ψ qp ( ξ , t ) has infinite norm, as in the ordinary case with no minimal length.

Nucleon-Nucleon Potentials and Computation of Scattering Phase Shifts

INDONESIAN JOURNAL OF APPLIED PHYSICS ◽

10.13057/ijap.v5i02.296 ◽

2015 ◽

Vol 5 (02) ◽

pp. 73

Author(s):

Jhasaketan Bhoi ◽

Ujjwal Laha

Keyword(s):

Wave Function ◽

Quantum Mechanics ◽

Ground State ◽

Function Method ◽

Nucleon Nucleon ◽

Phase Shifts ◽

Starting Point ◽

Phase Function Method ◽

Scattering Phase ◽

Scattering Phase Shifts

<p>By judicious exploitation of supersymmetry formalism of quantum mechanics higher partial wave nucleon-nucleon potentials are generated from its ground state interactions. The nuclear Hulthen potential and the corresponding ground state wave function with the parameters of Arnold and MacKellar are used as the starting point of our calculation. We compute the scattering phase shifts for our constructed potentials through Phase Function Method to examine the merit of our approach to the problem.</p>

Switching Internal Times and a New Perspective on the ‘Wave Function of the Universe’

Universe ◽

10.3390/universe5050116 ◽

2019 ◽

Vol 5 (5) ◽

pp. 116 ◽

Cited By ~ 13

Author(s):

Philipp Höhn

Keyword(s):

Wave Function ◽

Quantum Cosmology ◽

Reference System ◽

A Priori ◽

General Covariance ◽

Quantum Theories ◽

Dirac Quantization ◽

New Perspective ◽

Coordinate Changes ◽

Despite its importance in general relativity, a quantum notion of general covariance has not yet been established in quantum gravity and cosmology, where, given the a priori absence of coordinates, it is necessary to replace classical frames with dynamical quantum reference systems. As such, quantum general covariance bears on the ability to consistently switch between the descriptions of the same physics relative to arbitrary choices of quantum reference system. Recently, a systematic approach for such switches has been developed. It links the descriptions relative to different choices of quantum reference system, identified as the correspondingly reduced quantum theories, via the reference-system-neutral Dirac quantization, in analogy to coordinate changes on a manifold. In this work, we apply this method to a simple cosmological model to demonstrate how to consistently switch between different internal time choices in quantum cosmology. We substantiate the argument that the conjunction of Dirac and reduced quantized versions of the theory defines a complete relational quantum theory that not only admits a quantum general covariance, but, we argue, also suggests a new perspective on the ‘wave function of the universe’. It assumes the role of a perspective-neutral global state, without immediate physical interpretation that, however, encodes all the descriptions of the universe relative to all possible choices of reference system at once and constitutes the crucial link between these internal perspectives. While, for simplicity, we use the Wheeler-DeWitt formulation, the method and arguments might be also adaptable to loop quantum cosmology.

Quantum Cosmology of Quadratic f(R) Theories with a FRW Metric

Advances in Mathematical Physics ◽

10.1155/2017/1056514 ◽

2017 ◽

Vol 2017 ◽

pp. 1-5 ◽

Cited By ~ 2

Author(s):

V. Vázquez-Báez ◽

C. Ramírez

Keyword(s):

Wave Function ◽

Scalar Field ◽

Boundary Conditions ◽

Numerical Solution ◽

Quantum Cosmology ◽

Free Parameter ◽

Equations Of Motion ◽

Frw Metric ◽

We study the quantum cosmology of a quadratic fR theory with a FRW metric, via one of its equivalent Horndeski type actions, where the dynamic of the scalar field is induced. The classical equations of motion and the Wheeler-DeWitt equation, in their exact versions, are solved numerically. There is a free parameter in the action from which two cases follow: inflation + exit and inflation alone. The numerical solution of the Wheeler-DeWitt equation depends strongly on the boundary conditions, which can be chosen so that the resulting wave function of the universe is normalizable and consistent with Hermitian operators.