Perturbative effective field theory expansions for cosmological phase transitions

TL;DR

This paper introduces a perturbative effective field theory framework for analyzing cosmological phase transitions, improving accuracy and consistency by addressing issues like gauge dependence and infrared divergences, with applications to electroweak transitions.

Contribution

It develops a novel EFT expansion approach for cosmological phase transitions, bridging soft and ultrasoft scales, and offers a new method for two-step electroweak phase transition analysis.

Findings

Enhanced agreement with lattice simulations

New effective potential expressions for different phases

Reduced gauge and scale dependence in thermodynamic calculations

Abstract

Guided by previous non-perturbative lattice simulations of a two-step electroweak phase transition, we reformulate the perturbative analysis of equilibrium thermodynamics for generic cosmological phase transitions in terms of effective field theory (EFT) expansions. Based on thermal scale hierarchies, we argue that the scale of many interesting phase transitions is in-between the soft and ultrasoft energy scales, which have been the focus of studies utilising high-temperature dimensional reduction. The corresponding EFT expansions provide a handle to control the perturbative expansion, and allow us to avoid spurious infrared divergences, imaginary parts, gauge dependence and renormalisation scale dependence that have plagued previous studies. As a direct application, we present a novel approach to two-step electroweak phase transitions, by constructing separate effective descriptions for two consecutive transitions. Our approach provides simple expressions for effective potentials separately in different phases, a numerically inexpensive method to determine thermodynamics, and significantly improves agreement with the non-perturbative lattice simulations.