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.
- Received 21 July 2005
DOI:https://doi.org/10.1103/PhysRevD.73.044022
©2006 American Physical Society