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

On the transition from complex to real scalar fields in modern cosmology