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

G. A. Monerat, E. V. Corrêa Silva, G. Oliveira-Neto, L. G. Ferreira Filho, and N. A. Lemos
Phys. Rev. D 73, 044022 – Published 17 February 2006

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 Schrödinger 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.

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  • Received 21 July 2005

DOI:https://doi.org/10.1103/PhysRevD.73.044022

©2006 American Physical Society

Authors & Affiliations

G. A. Monerat1,*, E. V. Corrêa Silva1,†, G. Oliveira-Neto1,‡, L. G. Ferreira Filho2,§, and N. A. Lemos3,∥

  • 1Departamento de Matemática e Computação, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, Estrada Resende-Riachuelo, s/no, Morada da Colina, CEP 27523-000, Resende-RJ, Brazil
  • 2Departamento de Mecânica 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
  • 3Instituto de Física, Universidade Federal Fluminense, R. Gal. Milton Tavares de Souza s/no, Boa Viagem, CEP 24210-340, Niterói-RJ, Brazil

  • *Electronic address: monerat@uerj.br
  • Electronic address: evasquez@uerj.br
  • Electronic address: gilneto@fat.uerj.br
  • §Electronic address: gonzaga@fat.uerj.br
  • Electronic address: nivaldo@if.uff.br

Comments & Replies

Reply to “Comment on ‘Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation”’

N. A. Lemos, G. A. Monerat, E. V. Corrêa Silva, G. Oliveira-Neto, and L. G. Ferreira Filho
Phys. Rev. D 75, 068504 (2007)

Comment on “Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation”

Paolo Amore, Alfredo Aranda, Mayra Cervantes, J. L. Díaz-Cruz, and Francisco M. Fernández
Phys. Rev. D 75, 068503 (2007)

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Vol. 73, Iss. 4 — 15 February 2006

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