Non-minimally coupled scalar fields and the initial value problem in quantum gravity

The canonical quantization scheme for general relativity including a non-minimally coupled scalar field is investigated. It is demonstrated in detail how the signature of the Wheeler-DeWitt equation is changed thereby. This obscures the interpretation of the initial value problem in quantum gravity. A homogeneous and isotropic minisuperspace model is discussed and it is shown that it can become elliptical in certain regions of configuration space leading to the phenomenon of phase space tunnelling. (orig.)