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

G. A. Monerat, E. V. Corrêa Silva, G. Oliveira-Neto, L. G. Ferreira Filho, N. A. Lemos
2005 Brazilian journal of physics  
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
more » ... 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.
doi:10.1590/s0103-97332005000700024 fatcat:sfcidpz27bewtmngix6spazhgi