function of the universe using the path integral formulation but the recent attempts [@unru:gr-qc] suit nicely to the wormhole dominance proposal. The choosing of the paths in WKB formulation or in the Hartle-Hawking path integral formulation is another problem and needs to incorporate complex solutions/complex paths. This is the second problem. In the present work we do not delve into the controversy while keeping only a salient feature in evaluating the normalization constant of Schroedinger-Wheeler -DeWitt solution. The third problem is related to the association of the wavefunction to the Lorentzian condition in quantum gravity.

In the past the approach to quantum cosmology considered the behaviour of the wavefunction, as a function of the overall scalefactor, $a$ of the 3-metric $h_{ij}$, on the spacelike surface $\sum$. If the dependence on $a$ is exponential, the wavefunction corresponds to the Euclidean spacetime, while an oscillatory dependence on $a$ is interpreted as corresponding to a Lorentzian spacetime. However this distinction between exponential and oscillatory is not precise, and does not identify, which part of the wavefunction describes which physical situation [@bou:prd]. Technically it amounts to asking whether a given spacelike surface is a part of a Lorentzian spacetime or a Euclidean spacetime. Our 