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

TL;DR

This paper investigates the role of complex scalar fields in cosmology, showing they are significant during inflation but effectively real during dark energy dominance, using symmetry methods and quantum cosmology analysis.

Contribution

It demonstrates the transition from complex to real scalar fields in cosmology and applies Noether symmetry and semiclassical quantum cosmology to analyze this process.

Findings

Complex scalar fields are important during inflation.

The phase of the scalar field becomes constant in the dark energy era.

A potential with sixth and fourth powers of the scalar field is derived.

Abstract

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.