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

Journal Article · Wed Feb 15 04:00:00 EST 2006 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.73.044022· OSTI ID:20776760

Monerat, G A; Silva, E.V. Correa; Oliveira-Neto, G ^[1]; Filho, L.G. Ferreira ^[2]; Lemos, N A ^[3]

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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)

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.

• OSTI ID: 20776760
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 4 Vol. 73; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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