QUANTUM COSMOLOGY WITH A COMPLEX FIELD

The classical and quantum cosmology of a complex scalar field is considered. In this model the Euclidean region contour in the minisuperspace is generally a closed curve. The wave function of the Universe, evaluated in the WKB approximation, propagates through scattering or tunneling from the initial classical state to the final classical state. The probability distribution for the Vilenkin choice of boundary conditions shows that the classical universe preferentially starts with a large matter content only if the cosmological constant is set to zero.