Wave funcitions for highly anisotropic homogeneous cosmologies

The canonical quantization of homogeneous cosmologies is considered in the high anisotropic limit. Exact wave functions are found in this limit when the momentum constraints are reduced at the classical level. Lorentzian solutions that represent tunnelling from classically forbidden regimes are identified. Solutions to the modified Wheeler-DeWitt equation are also found for the vacuum Bianchi IX model when a quantum reduction of the momentum constraints is considered.