Cosmological phase transitions at three loops: the final verdict on perturbation theory

TL;DR

This paper computes the three-loop finite-temperature effective potential for gauge-Higgs theories, providing the most precise perturbative predictions for cosmological phase transitions and their gravitational wave signatures, and confirms these with lattice results.

Contribution

It delivers the first complete three-loop (N$^4$LO) calculation of the effective potential for gauge-Higgs theories, advancing the precision of cosmological phase transition predictions.

Findings

Excellent agreement with lattice results.

Final perturbative predictions for phase transition strength.

Provides key inputs for gravitational wave signal estimates.

Abstract

We complete the perturbative program for equilibrium thermodynamics of cosmological first-order phase transitions by determining the finite-temperature effective potential of gauge-Higgs theories at next-to-next-to-next-to-next-to-leading order (N$^4$LO). The computation of the three-loop effective potential required to reach this order is extended to generic models in dimensionally reduced effective theories in a companion article. Our N$^4$LO result is the last perturbative order before confinement renders electroweak gauge-Higgs theories non-perturbative at four loops. By contrasting our analysis with non-perturbative lattice results, we find a remarkable agreement. As a direct application for predictions of gravitational waves produced by a first-order transition, our computation provides the final fully perturbative results for the phase transition strength and speed of sound.