Introduction

Developments in physics on the smallest and largest scales (elementary particle theory and cosmology) over the past several decades have provided strong evidence for the hot Big Bang theory of the early Universe and for gauge field models of elementary particle interactions, particularly as embodied in the Standard Model of elementary particle physics.

In adopting these two theories it is very difficult to avoid the phenomenon of cosmological vacuum phase transitions. Such phase transitions arise because of the temperature dependence of the Higgs field potential. This potential plays several roles within gauge field theories, from providing a mechanism for spontaneous symmetry breaking to providing a possible vacuum energy density. The Higgs field potential (which we shall henceforth label as U(φ), where φ represents the field) at high temperature possesses a single vacuum state, which we may arbitrarily choose to be located at φ = 0. The Higgs potential undergoes a continuous evolution as the temperature is changed and at low temperatures the potential may possess multiple vacuum states (i.e., multiple minima). The nature of the transition from the high temperature vacuum state to the low temperature vacuum state will depend upon the shape of the potential during the course of its evolution. It is possible that the Higgs field will undergo a classical “rolling” evolution between the initial and final vacuum states.