Notes on the quantization of FRW model in the presence of a cosmological constant and radiation

AUTOR(ES)

Monerat, G. A., Silva, E. V. Corrêa, Oliveira-Neto, G., Ferreira Filho, L. G., Lemos, N. A.

FONTE

Brazilian Journal of Physics

DATA DE PUBLICAÇÃO

2005-12

RESUMO

In the present work, we use the formalism of quantum general relativity in order to quantize a Friedmann-Robertson-Walker model in the presence of a negative cosmological constant and radiation. The model has spatial sections with positive constant curvature. The wave-function of the model satisfies a Wheeler-DeWitt equation, for the scale factor, which has the form of the Schrödinger's equation for the quartic anharmonic oscillator. We find the 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 evaluating the time-dependent, expected value of the scale factor. We find that, the expected value of the scale factor oscillates between maximum and minimum values. Since the scale factor never vanishes, we conclude that the model does not have a singularity.

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