Quantization of Friedmann-Robertson-Walker Spacetimes in the Presence of a Cosmological Constant and Stiff Matter

In the present work, we study the quantum cosmology description of two Friedmann-Robertson-Walker models in the presence of a stiff matter perfect fluid and a negative cosmological constant. The models differ from each other by the constant curvature of the spatial sections, taken to be either positive or zero. We work in the Schutz's variational formalism, quantizing the models and obtaining the appropriate Wheeler-DeWitt equations. In these models there are bound states. Therefore, we compute, for each one, the discrete energy spectrum and the corresponding eigenfunctions. After that, we use the eigenfunctions in order to construct wave packets and evaluate the time-dependent expectation values of the scale factors. Each model shows bounded oscillations for the expectation value of the scalar factor, which is never zero, which can be interpreted as an initial indication that these models may not have singularities at the quantum level.