Abstract

In this paper, the classical and quantum solutions of some axisymmetrlc cosmologies coupled to a massless scalar field are studied in the context of mimsuperspace approximation. In these models, the singular nature of the Lagrangians entails a search for possible conditional symmetries. These have been proven to be the simultaneous conformal syninwtries of the supermetric and the super potential. The quantization is performed by adopting the Dirac proposal for constrained systems, i.e. promoting the first-class constraints to operators annihilating the wave function. To further enrich the approach, we follow and impose the operators related to the classical conditional symmetries on the wave function. These additional equations select particular solutions of the Wheeler -DeWitt equation. In order to gain some physical insight from the quantization of these cosmological systems, we perform a semiclassical analysis following the Bohmian approach to gum:AM:11 theory. The generic result is that, in all but one model, one can find appropriate ranges of the parameters, so that the emerging semiclassical geometries are non-singular. An attempt for physical interpretation involves the study of the effective energy-momentum tensor which corresponds to an imperfect fluid.