  We study some problems arising from the introduction of a complex scalar
field in cosmology, modelling its possible behaviors in both the inflationary
and dark energy stages of the universe. Such examples contribute to show that,
while the complex nature of the scalar field can be indeed important during
inflation, it loses its meaning in the later dark-energy dominated era of
cosmology, when the phase of the complex field is practically constant, and
there is indeed a transition from complex to real scalar field. In our
considerations, the Noether symmetry approach turns out to be a useful tool
once again. We arrive eventually at a potential containing the sixth and fourth
powers of the scalar field, and the resulting semiclassical quantum cosmology
is studied to gain a better understanding of the inflationary stage.
