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Title: Reply to 'Comment on 'Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation''

Abstract

The previous Comment contains a valid criticism of the numerical precision of the results reported in a recent paper of ours, as well as fresh ideas on how to characterize a quantum cosmological singularity. However, we argue that, contrary to what is suggested in the Comment, the quantum cosmological models we studied show hardly any sign of singular behavior.

Authors:
; ; ; ;  [1];  [2];  [2]
  1. Instituto de Fisica, Universidade Federal Fluminense, R. Gal. Milton Tavares de Souza s/n, CEP 24210-340, Niteroi, RJ (Brazil)
  2. (Brazil)
Publication Date:
OSTI Identifier:
21020226
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.75.068504; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACCURACY; COSMOLOGICAL CONSTANT; COSMOLOGICAL MODELS; COSMOLOGY; QUANTIZATION; QUANTUM FIELD THEORY; SINGULARITY; SPACE-TIME

Citation Formats

Lemos, N. A., Monerat, G. A., Silva, E. V. Correa, Oliveira-Neto, G., Filho, L. G. Ferreira, Departamento de Matematica e Computacao, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, Estrada Resende-Riachuelo s/n, CEP 27523-000, Resende, RJ, and Departamento de Mecanica e Energia, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, Estrada Resende-Riachuelo s/n, CEP 27523-000, Resende, RJ. Reply to 'Comment on 'Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation''. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.068504.
Lemos, N. A., Monerat, G. A., Silva, E. V. Correa, Oliveira-Neto, G., Filho, L. G. Ferreira, Departamento de Matematica e Computacao, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, Estrada Resende-Riachuelo s/n, CEP 27523-000, Resende, RJ, & Departamento de Mecanica e Energia, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, Estrada Resende-Riachuelo s/n, CEP 27523-000, Resende, RJ. Reply to 'Comment on 'Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation''. United States. doi:10.1103/PHYSREVD.75.068504.
Lemos, N. A., Monerat, G. A., Silva, E. V. Correa, Oliveira-Neto, G., Filho, L. G. Ferreira, Departamento de Matematica e Computacao, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, Estrada Resende-Riachuelo s/n, CEP 27523-000, Resende, RJ, and Departamento de Mecanica e Energia, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, Estrada Resende-Riachuelo s/n, CEP 27523-000, Resende, RJ. Thu . "Reply to 'Comment on 'Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation''". United States. doi:10.1103/PHYSREVD.75.068504.
@article{osti_21020226,
title = {Reply to 'Comment on 'Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation''},
author = {Lemos, N. A. and Monerat, G. A. and Silva, E. V. Correa and Oliveira-Neto, G. and Filho, L. G. Ferreira and Departamento de Matematica e Computacao, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, Estrada Resende-Riachuelo s/n, CEP 27523-000, Resende, RJ and Departamento de Mecanica e Energia, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, Estrada Resende-Riachuelo s/n, CEP 27523-000, Resende, RJ},
abstractNote = {The previous Comment contains a valid criticism of the numerical precision of the results reported in a recent paper of ours, as well as fresh ideas on how to characterize a quantum cosmological singularity. However, we argue that, contrary to what is suggested in the Comment, the quantum cosmological models we studied show hardly any sign of singular behavior.},
doi = {10.1103/PHYSREVD.75.068504},
journal = {Physical Review. D, Particles Fields},
number = 6,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • The quantization of the Friedmann-Robertson-Walker spacetime in the presence of a negative cosmological constant was used in a recent paper to conclude that there are solutions that avoid singularities (big bang-big crunch) at the quantum level. We show that a proper study of their model does not indicate that it prevents the occurrence of singularities at the quantum level, in fact the quantum probability of such event is larger than the classical one. Our numerical simulations based on the powerful variational sinc collocation method (VSCM) also show that the precision of the results of that paper is much lower thanmore » the 20 significant digits reported by the authors.« less
  • In the present work, we quantize three Friedmann-Robertson-Walker models in the presence of a negative cosmological constant and radiation. The models differ from each other by the constant curvature of their spatial sections, which may be positive, negative or zero. They give rise to Wheeler-DeWitt equations for the scale factor which have the form of the Schroedinger equation for the quartic anharmonic oscillator. We find their eigenvalues and eigenfunctions by using a method first developed by Chhajlany and Malnev. After that, we use the eigenfunctions in order to construct wave packets for each case and evaluate the time-dependent expectation valuemore » of the scale factors, which are found to oscillate between finite maximum and minimum values. Since the expectation values of the scale factors never vanish, we have an initial indication that these models may not have singularities at the quantum level.« less
  • The expansion of the wave function of a quantum Friedmann-Robertson-Walker cosmology minimally coupled to a scalar field with a power-law potential by its scalar-field part decouples the gravitational-field part into an infinite system of linear homogeneous differential equations (equivalent to a matrix equation). The solutions for the gravitational-field part are found in the product integral formulation. It is shown that there exists a spectrum of the wave functions exponentially damped for large three-geometries under the condition that the cosmological constant should vanish. These are interpeted as the Hawking-Page wormholes.
  • In some interesting work of James Lidsey, the dynamics of Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology with positive curvature and a perfect fluid matter source is shown to be modeled in terms of a time-dependent, harmonically trapped Bose-Einstein condensate. In the present work, we extend this dynamic correspondence to both FLRW and Bianchi I cosmologies in arbitrary dimension, especially when a cosmological constant is present.
  • We consider a flat cosmological model with a free massless scalar field and the cosmological constant {Lambda} in the framework of loop quantum cosmology. The scalar field plays the role of an intrinsic time. We apply the reduced phase space approach. The dynamics of the model is solved analytically. We identify elementary observables and their algebra. The compound physical observables like the volume and the energy density of matter field are analyzed. Both compound observables are bounded and oscillate in the {Lambda}<0 case. The energy density is bounded and oscillates in the {Lambda}>0 case. However, the volume is unbounded frommore » above, but periodic. The difference between standard and nonstandard loop quantum cosmology is described.« less