Cosmological Inflation as a Quantum Phase Transition

Abstract

The aim of this paper is to clarify the understanding of the fundamental dynamics in the time evolution of phase transitions based on quantum field theory. This formalism is particularly necessary for the inflationary phase transition in the early Universe when it is quenched in the effectively zero temperature phase. In this situation, quantum fluctuations dominate thermal fluctuations. We first critically review the standard scenario of the inflationary phase transition: the problem of defining the order parameter, the problem of complex and non-convex effective potentials etc. In order to solve these fundamental problems, we develop the formalism of non-equilibrium quantum firld theory. In the process, we a) define the local order parameter relevant for the dynamics of phase transitions in this formalism, and compare this local order parameter with the ordinary global order parameter, b) systematically describe the dissipation and fluctuation effects induced from the special type of radiative corrections (in-in formalism of quantum field theory), c) derive the equation of motion for the local order parameter which becomes a generalized Langevin-type stochastic differential equation, d) argue that dissipative effects destroy the quantum coherence of the system and demonstrate that the ordinary quantum theory based on a single Hilbert space is not sufficient, e) expound upon the validity of using the effective potential for the dynamics of phase transitions, and finally, f) demonstrate that the unstable self-coupling scalar field can actually induce the dissipative effects, and derive the equation of motion for the order parameter.