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Title: Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation

Abstract

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 value 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.

Authors:
; ;  [1];  [2];  [3]
  1. Departamento de Matematica e Computacao, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, Estrada Resende-Riachuelo, s/no, Morada da Colina, CEP 27523-000, Resende-RJ (Brazil)
  2. Departamento de Mecanica e Energia, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, Estrada Resende-Riachuelo, s/no, Morada da Colina, CEP 27523-000 , Resende-RJ (Brazil)
  3. Instituto de Fisica, Universidade Federal Fluminense, R. Gal. Milton Tavares de Souza s/no, Boa Viagem, CEP 24210-340, Niteroi-RJ (Brazil)
Publication Date:
OSTI Identifier:
20776760
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.73.044022; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANHARMONIC OSCILLATORS; COSMOLOGICAL CONSTANT; COSMOLOGY; EIGENFUNCTIONS; EIGENVALUES; EXPECTATION VALUE; QUANTIZATION; SCHROEDINGER EQUATION; SINGULARITY; SPACE-TIME; TIME DEPENDENCE; WAVE FUNCTIONS; WAVE PACKETS

Citation Formats

Monerat, G A, Silva, E.V. Correa, Oliveira-Neto, G, Filho, L.G. Ferreira, and Lemos, N A. Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation. United States: N. p., 2006. Web. doi:10.1103/PhysRevD.73.044022.
Monerat, G A, Silva, E.V. Correa, Oliveira-Neto, G, Filho, L.G. Ferreira, & Lemos, N A. Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation. United States. https://doi.org/10.1103/PhysRevD.73.044022
Monerat, G A, Silva, E.V. Correa, Oliveira-Neto, G, Filho, L.G. Ferreira, and Lemos, N A. 2006. "Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation". United States. https://doi.org/10.1103/PhysRevD.73.044022.
@article{osti_20776760,
title = {Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation},
author = {Monerat, G A and Silva, E.V. Correa and Oliveira-Neto, G and Filho, L.G. Ferreira and Lemos, N A},
abstractNote = {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 value 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.},
doi = {10.1103/PhysRevD.73.044022},
url = {https://www.osti.gov/biblio/20776760}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 4,
volume = 73,
place = {United States},
year = {2006},
month = {2}
}