On the perturbative expansion at high temperature and implications for cosmological phase transitions

TL;DR

This paper examines the convergence issues of perturbative expansions at high temperature, highlighting the need for two-loop calculations to reduce uncertainties in cosmological phase transition predictions.

Contribution

It demonstrates how to restore renormalisation scale independence at high temperature by incorporating two-loop computations, improving theoretical predictions for cosmological phase transitions.

Findings

Renormalisation scale dependence increases at high temperature.

Two-loop calculations are necessary for scale independence.

Improved predictions reduce uncertainties in gravitational wave signals.

Abstract

We revisit the perturbative expansion at high temperature and investigate its convergence by inspecting the renormalisation scale dependence of the effective potential. Although at zero temperature the renormalisation group improved effective potential is scale independent at one-loop, we show how this breaks down at high temperature, due to the misalignment of loop and coupling expansions. Following this, we show how one can recover renormalisation scale independence at high temperature, and that it requires computations at two-loop order. We demonstrate how this resolves some of the huge theoretical uncertainties in the gravitational wave signal of first-order phase transitions, though uncertainties remain stemming from the computation of the bubble nucleation rate.