Perturbative nonequilibrium dynamics of phase transitions in an expanding universe

TL;DR

This paper develops a perturbative framework for analyzing nonequilibrium phase transition dynamics in an expanding universe, incorporating dissipative effects and spontaneous symmetry breaking within a consistent approximation scheme.

Contribution

It introduces a novel perturbative method that describes nonequilibrium states with finite-width quasiparticles in an expanding universe, addressing symmetry breaking and dissipation.

Findings

Derived Feynman rules for nonequilibrium dynamics in an expanding universe.

Explicit one-loop calculations of quasiparticle masses and field equations.

Discussed ambiguities in perturbative series and procedures for matching symmetric and broken states.

Abstract

A complete set of Feynman rules is derived, which permits a perturbative description of the nonequilibrium dynamics of a symmetry-breaking phase transition in $\lambda\phi^4$ theory in an expanding universe. In contrast to a naive expansion in powers of the coupling constant, this approximation scheme provides for (a) a description of the nonequilibrium state in terms of its own finite-width quasiparticle excitations, thus correctly incorporating dissipative effects in low-order calculations, and (b) the emergence from a symmetric initial state of a final state exhibiting the properties of spontaneous symmetry breaking, while maintaining the constraint $<\phi>\equiv 0$. Earlier work on dissipative perturbation theory and spontaneous symmetry breaking in Minkowski spacetime is reviewed. The central problem addressed is the construction of a perturbative approximation scheme which treats the initial symmetric state in terms of the field $\phi$, while the state that emerges at later times is treated in terms of a field $\zeta$, linearly related to $\phi^2$. The connection between early and late times involves an infinite sequence of composite propagators. Explicit one-loop calculations are given of the gap equations that determine quasiparticle masses and of the equation of motion for $<\phi^2(t)>$ and the renormalization of these equations is described. The perturbation series needed to describe the symmetric and broken-symmetry states are not equivalent, and this leads to ambiguities intrinsic to any perturbative approach. These ambiguities are discussed in detail and a systematic procedure for matching the two approximations is described.