Abstract
We discuss the issue of unitarity in particular quantum cosmological models with scalar field. The time variable is recovered, in this context, by using the Schutz's formalism for a radiative fluid. Two cases are considered: a phantom scalar field and an ordinary scalar field. For the first case, it is shown that the evolution is unitary provided a convenient factor ordering and inner product measure are chosen; the same happens for the ordinary scalar field, except for some special cases for which the Hamiltonian is not self-adjoint but admits a self-adjoint extension. In all cases, even for those cases not exhibiting unitary evolution, the formal computation of the expectation value of the scale factor indicates a non-singular bounce. The importance of the unitary evolution in quantum cosmology is briefly discussed.
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