NÖTHER’S SYMMETRIES IN QUANTUM COSMOLOGY

1994 ◽  
Vol 03 (03) ◽  
pp. 609-621 ◽  
Author(s):  
SALVATORE CAPOZZIELLO ◽  
RUGGIERO DE RITIS ◽  
PAOLO SCUDELLARO
Keyword(s):  
Wave Function ◽  
Scalar Field ◽  
Quantum Cosmology ◽  
Selection Rule ◽  
Theories Of Gravity ◽  
The Universe ◽  
Semiclassical Regime

We construct minisuperspace models for a class of theories of gravity nonminimally coupled with a scalar field. We show that when a Nöther symmetry exists, it is always possible to integrate the Wheeler-DeWitt equation and recover the semiclassical regime for the wave function of the universe. In this sense, we can interpret the Nöther symmetries as a selection rule in the philosophy of the so called Hartle criterion: when they exist, it is possible to select classical universes.

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.

QUANTUM COSMOLOGY WITH A NONLINEAR BORN–INFELD TYPE SCALAR FIELD

1999 ◽  
Vol 08 (05) ◽  
pp. 625-634 ◽  
Author(s):  
H. Q. LU ◽  
T. HARKO ◽  
K. S. CHENG
Keyword(s):  
Wave Function ◽  
Scalar Field ◽  
Quantum Cosmology ◽  
Vacuum Energy ◽  
Quantum Model ◽  
Inflationary Universe ◽  
Cosmological Scale ◽  
Scale Factors ◽  
Nonlinear Scalar Field ◽  
The Universe

A quantum model of gravitation interacting with a Born–Infeld type nonlinear scalar field φ is considered. The corresponding Wheeler–DeWitt equation can be solved analytically for both large and small [Formula: see text]. In the extreme limits of small and large cosmological scale factors the wave function of the Universe can also be obtained by applying the methods developed by Vilenkin and Hartle and Hawking. An inflationary Universe is predicted with the largest possible vacuum energy and the largest interaction between the particles of the nonlinear scalar field.

scholarly journals Wave Packet in Quantum Cosmology and Definition of Semiclassical Time

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 ◽  
The Universe

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.

scholarly journals EMERGENT UNIVERSE WITH EXOTIC MATTER IN LOOP QUANTUM COSMOLOGY, DGP BRANE-WORLD AND KALUZA–KLEIN COSMOLOGY

2012 ◽  
Vol 27 (33) ◽  
pp. 1250189 ◽  
Author(s):  
PRABIR RUDRA
Keyword(s):  
Scalar Field ◽  
Quantum Cosmology ◽  
Brane World ◽  
Loop Quantum Cosmology ◽  
Tachyonic Field ◽  
Normal Matter ◽  
Emergent Scenario ◽  
Phantom Scalar ◽  
The Universe ◽  
Kaluza Klein

In this work we have investigated the emergent scenario of the Universe described by loop quantum cosmology model, DGP brane model and Kaluza–Klein cosmology. Scalar field along with barotropic fluid as normal matter is considered as the matter content of the Universe. In loop quantum cosmology it is found that the emergent scenario is realized with the imposition of some conditions on the value of the density of normal matter in case of normal and phantom scalar field. This is a surprising result indeed considering the fact that scalar field is the dominating matter component! In case of tachyonic field, emergent scenario is realized with some constraints on the value of ρ1 for both normal and phantom tachyon. In case of DGP brane-world realization of an emergent scenario is possible almost unconditionally for normal and phantom fields. Plots and table have been generated to testify this fact. In case of tachyonic field emergent scenario is realized with some constraints on [Formula: see text]. In Kaluza–Klein cosmology emergent scenario is possible only for a closed Universe in case of normal and phantom scalar field. For a tachyonic field, realization of emergent Universe is possible for all models (closed, open and flat).

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 Phantom energy-dominated universe as a transient stage in f(R) cosmology

2019 ◽  
Vol 28 (10) ◽  
pp. 1950124 ◽  
Author(s):  
P. H. R. S. Moraes ◽  
P. K. Sahoo ◽  
Barkha Taori ◽  
Parbati Sahoo
Keyword(s):  
Quantum Cosmology ◽  
Bianchi Type ◽  
Phantom Energy ◽  
Type I ◽  
Dark Sector ◽  
Transient Stage ◽  
Standard Cosmology ◽  
Theories Of Gravity ◽  
The Universe ◽  
Einstein’S General Relativity

The [Formula: see text] theories of gravity are the most popular, simple and well-succeeded extension of Einstein’s General Relativity. They can account for some observational issues of standard cosmology with no need for evoking the dark sector of the universe. In the present paper, we will investigate LRS Bianchi type-I spacetime in [Formula: see text] gravity theory within the phantom energy-dominated era. We show that in this formalism the phantom energy-dominated universe is a transient stage and in the further stage of the universe dynamics, it is dominated, once again, by dark energy. Such an important feature is obtained from the model, rather than imposed to it, and may have a relation to loop quantum cosmology.

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 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.

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.

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