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

We introduce a complex scalar field in cosmology, modeling its possible behaviors in both the inflationary and dark energy stages of the universe. We contribute to show that the complex nature of the scalar field oses 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. Here, the Noether symmetry approach turns out to be a useful tool again. We arrive eventually at a potential containing the 6th and 4th powers of the scalar field, and the resulting semiclassical quantum cosmology is studied for understanding inflation.