Cosmological Adiabatic Geometric Phase of a Scalar Field in a Bianchi Spacetime

TL;DR

This paper explores the adiabatic geometric phases of a scalar field in Bianchi cosmological models, revealing no phases in type I but complex non-Abelian phases in type IX, linked to nuclear quadrupole interactions.

Contribution

It introduces a two-component Klein-Gordon formulation to analyze geometric phases in Bianchi models, highlighting the absence in type I and the presence of non-Abelian phases in type IX.

Findings

No adiabatic geometric phases in Bianchi type I.

Non-Abelian phases can occur in Bianchi type IX.

Equivalence to nuclear quadrupole interaction problem.

Abstract

A two-component formulation of the Klein-Gordon equation is used to investigate the cyclic and noncyclic adiabatic geometric phases due to spatially homogeneous (Bianchi) cosmological models. It is shown that no adiabatic geometric phases arise for Bianchi type I models. For general Bianchi type IX models the problem of the adiabatic geometric phase is shown to be equivalent to the one for nuclear quadrupole interactions of a spin. For these models nontrivial non-Abelian adiabatic geometrical phases may occur in general.