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

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.

Automated summary

This study revisits the perturbative expansion at high temperature and investigates the convergence by examining the renormalisation scale dependence of the effective potential. The renormalisation group improved effective potential is scale independent at zero temperature but breaks down at high temperature due to misalignment of loop and coupling expansions. Recovering renormalisation scale independence at high temperature requires computations at two-loop order and helps resolve theoretical uncertainties in the gravitational wave signal of first-order phase transitions, although uncertainties remain from the computation of the bubble nucleation rate.