QUANTUM COSMOLOGY OF KANTOWSKI-SACHS-LIKE MODELS

The Wheeler-DeWitt equation for a class of Kantowski-Sachs-like models is completely solved. The generalized models include the Kantowski-Sachs model with cosmological constant and pressureless dust. Likewise contained is a joined model which consists of a Kantowski-Sachs cylinder inserted between two FRW half-spheres. The (second-order) WKB approximation is exact for the wavefunctions of the complete set and this facilitates the product structure of the wavefunction for the joined model. In spite of the product structure the wavefunction cannot be interpreted as admitting no correlations between the different regions. This problem is due to the joining procedure and may therefore be present for all joined models. Finally, the symmetric initial condition for the wavefunction is analysed and compared with the 'no-boundary' condition. The consequences of the different boundary conditions for the arrow of time are briefly mentioned.