Classical limit in quantum cosmology: Quantum mechanics and the Wigner function

We study the classical limit of quantum mechanics as applied to quantum cosmology. Conventional wisdom regards the peaking of the Wigner function of the Universe around a classical trajectory as being a quantum prediction of that trajectory. We show that, with quantum interference correctly taken into account, the hoped for "classical correlation" does not exist. There are, therefore, serious difficulties with the notion that a pure quantum state has a classical limit relevant to the description of our world. Some form of quantum decoherence appears necessary for a strict classical limit to exist. This alternative is briefly discussed.