QUANTUM COSMOLOGY WITH A COMPLEX FIELD

The classical and quantum cosmology of a complex scalar field is consi dered. In this model the Euclidean region contour in the minisuperspac e is generally a closed curve. The wave function of the Universe, eval uated in the WKB approximation, propagates through scattering or tunne ling from the initial classical state to the final classical state. Th e probability distribution for the Vilenkin choice of boundary conditi ons shows that the classical universe preferentially starts with a lar ge matter content only if the cosmological constant is set to zero.