SINGULARITIES AND THE CLASSICAL LIMIT IN QUANTUM COSMOLOGY WITH SCALAR FIELDS

Minisuperspace models derived from Kaluza-Klein theories and low-energ y string theory are studied. They are equivalent to one and two minima lly coupled scalar fields. The general classical and quantum solutions are obtained. A Gaussian superposition of WKB solutions is constructe d. Contrary to what is usually expected, these states are sharply peak ed around the classical trajectories only for small values of the scal e factor. This behavior is confirmed in the framework of the causal in terpretation: the Bohmian trajectories of many quantum states are clas sical for small values of the scale factor but present quantum behavio r when the scale factor becomes large. A consequence of this fact is t hat these states present an initial singularity. However, there are so me particular superpositions of these wave functions which have Bohmia n trajectories without singularities. There are also singular Bohmian trajectories with a short period of inflation which grow forever. We c ould not find any nonsingular trajectory which grows to the size of ou r universe.