BOUNCING AND QUANTUM THEORY

2011 ◽  
Vol 26 (22) ◽  
pp. 3801-3812
Author(s):  
NELSON PINTO-NETO
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
Power Spectrum ◽  
Quantum Cosmology ◽  
Cosmological Perturbations ◽  
Simple Equations ◽  
The Universe ◽  
Inflationary Models

In this contribution I will present a review about bouncing models arriving from quantum cosmology and show how one can describe the evolution of quantum cosmological perturbations on them. I will discuss the important role played by the choice of the precise quantum theory one selects to interpret the wave function of the Universe in order to obtain simple equations for the evolution of quantum perturbations on these quantum cosmological backgrounds. I will present the predictions of these models concerning the power spectrum of cosmological perturbations and how they can be compared with the usual results obtained from inflationary models. Finally, I will present the new implications of these results for quantum theory.

BOUNCING AND QUANTUM THEORY

2011 ◽  
Vol 03 ◽  
pp. 183-194
Author(s):  
NELSON PINTO-NETO
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
Power Spectrum ◽  
Quantum Cosmology ◽  
Cosmological Perturbations ◽  
Simple Equations ◽  
The Universe ◽  
Inflationary Models

In this contribution I will present a review about bouncing models arriving from quantum cosmology and show how one can describe the evolution of quantum cosmological perturbations on them. I will discuss the important role played by the choice of the precise quantum theory one selects to interpret the wave function of the Universe in order to obtain simple equations for the evolution of quantum perturbations on these quantum cosmological backgrounds. I will present the predictions of these models concerning the power spectrum of cosmological perturbations and how they can be compared with the usual results obtained from inflationary models. Finally, I will present the new implications of these results for quantum theory.

INTERPRETATION AND PREDICTABILITY OF QUANTUM MECHANICS AND QUANTUM COSMOLOGY

1988 ◽  
Vol 03 (07) ◽  
pp. 645-651 ◽  
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.

scholarly journals Quantum cosmology with dynamical vacuum in a minimal-length scenario

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 ◽  
The Universe

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.

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

Universe ◽  
2019 ◽  
Vol 5 (5) ◽  
pp. 116 ◽  
Author(s):  
Philipp Höhn
Keyword(s):  
Wave Function ◽  
Quantum Cosmology ◽  
Reference System ◽  
A Priori ◽  
General Covariance ◽  
Quantum Theories ◽  
Dirac Quantization ◽  
New Perspective ◽  
Coordinate Changes ◽  
The Universe

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.

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

2017 ◽  
Vol 2017 ◽  
pp. 1-5 ◽  
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 ◽  
The Universe

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.

scholarly journals SUPERSYMMETRIC QUANTUM COSMOLOGY FOR BIANCHI CLASS A MODELS

1998 ◽  
Vol 07 (05) ◽  
pp. 701-712 ◽  
Author(s):  
ALFREDO MACÍAS ◽  
ECKEHARD W. MIELKE ◽  
JOSÉ SOCORRO
Keyword(s):  
Wave Function ◽  
Quantum Cosmology ◽  
Rest Frame ◽  
Matrix Representation ◽  
Canonical Theory ◽  
Class A ◽  
Spatially Homogeneous ◽  
The Universe ◽  
Homogeneous Cosmologies

The canonical theory of [Formula: see text] supergravity, with a matrix representation for the gravitino covector–spinor, is applied to the Bianchi class A spatially homogeneous cosmologies. The full Lorentz constraint and its implications for the wave function of the universe are analyzed in detail. We found that in this model no physical states other than the trivial "rest frame" type occur.

scholarly journals Hartle-Hawking wave function and large-scale power suppression of CMB

2018 ◽  
Vol 168 ◽  
pp. 08002
Author(s):  
Dong-han Yeom
Keyword(s):  
Wave Function ◽  
Power Spectrum ◽  
Quantum Cosmology ◽  
Large Scale ◽  
Integral Approach ◽  
Scale Invariant ◽  
Instanton Solution ◽  
Euclidean Wormholes ◽  
Potential Parameters ◽  
Suitable Potential

In this presentation, we first describe the Hartle-Hawking wave function in the Euclidean path integral approach. After we introduce perturbations to the background instanton solution, following the formalism developed by Halliwell-Hawking and Laflamme, one can obtain the scale-invariant power spectrum for small-scales. We further emphasize that the Hartle-Hawking wave function can explain the large-scale power suppression by choosing suitable potential parameters, where this will be a possible window to confirm or falsify models of quantum cosmology. Finally, we further comment on possible future applications, e.g., Euclidean wormholes, which can result in distinct signatures to the power spectrum.

scholarly journals The de Broglie–Bohm Quantum Theory and Its Application to Quantum Cosmology

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 134
Author(s):  
Nelson Pinto-Neto
Keyword(s):  
Quantum Theory ◽  
Configuration Space ◽  
Physical System ◽  
Quantum Cosmology ◽  
Dynamical Theory ◽  
Cosmological Models ◽  
Cosmological Perturbations ◽  
Alternative Description ◽  
Quantum Phenomena ◽  
De Broglie Bohm

We review the de Broglie–Bohm quantum theory. It is an alternative description of quantum phenomena in accordance with all the quantum experiments already performed. Essentially, it is a dynamical theory about objectively real trajectories in the configuration space of the physical system under investigation. Hence, it is not necessarily probabilistic, and it dispenses with the collapse postulate, making it suitable to be applied to cosmology. The emerging cosmological models are usually free of singularities, with a bounce connecting a contracting era with an expanding phase, which we are now observing. A theory of cosmological perturbations can also be constructed under this framework, which can be successfully confronted with current observations, and can complement inflation or even be an alternative to it.

QUANTUM COSMOLOGY IN ANISOTROPIC COSMOLOGICAL MODELS WITH SCALAR–TENSOR THEORIES

2001 ◽  
Vol 10 (06) ◽  
pp. 943-956
Author(s):  
SUBENOY CHAKRABORTY
Keyword(s):  
Wave Function ◽  
Quantum Cosmology ◽  
Classical Limit ◽  
Cosmological Models ◽  
Integral Formulation ◽  
Causal Interpretation ◽  
Anisotropic Cosmological Models ◽  
Bohmian Trajectories ◽  
The Universe ◽  
Method Of Steepest Descent

This paper deals with quantum cosmological phenomena in anisotropic cosmological models with nonminimally coupled scalor field. With proper transformation of the field variables, the Wheeler–Dewitt (WD) equation looks simple in form and solutions are obtained using separable form of the wave function. Using part integral formulation, the wave function of the Universe has been evaluated by the method of steepest descent. Finally, the causal interpretation has been done using quantum Bohmian trajectories and also we study the classical limit of some particular solutions of these quantum models.

On the meaning of the wave function of the Universe

2019 ◽  
Vol 28 (13) ◽  
pp. 1941009 ◽  
Author(s):  
Tatyana P. Shestakova
Keyword(s):  
Wave Function ◽  
Quantum Cosmology ◽  
Quantum Processes ◽  
Extended Phase ◽  
Quantization Of Gravity ◽  
Present Universe ◽  
Objective Description ◽  
The Universe ◽  
Quantum Geometrodynamics ◽  
Space Approach

The meaning of the wave function of the Universe was actively discussed in 1980s. In most works on quantum cosmology, it is accepted that the wave function is a probability amplitude for the Universe to have some space geometry, or to be found in some point of the Wheeler superspace. It seems that the wave function gives maximally objective description compatible with quantum theory. However, the probability distribution does not depend on time and does not take into account the existing of our macroscopic evolving Universe. What we wish to know is how quantum processes in the Early Universe determined the state of the present Universe in which we are able to observe macroscopic consequences of these quantum processes. As an alternative to the Wheeler–DeWitt quantum geometrodynamics, we consider the picture that can be obtained in the extended phase space approach to quantization of gravity. The wave function in this approach describes different states of the Universe which correspond to different stages of its evolution.

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