Cosmological phase transitions without high-temperature expansions

TL;DR

This paper develops a new perturbative framework for accurately computing thermodynamic properties of cosmological phase transitions across all mass regimes, avoiding high-temperature approximations and enabling precise predictions for beyond-Standard-Model physics.

Contribution

It introduces a unified approach using the full four-dimensional resummed thermal effective potential and Loop-Tree Duality, allowing high-loop calculations without high-temperature expansions.

Findings

Performed a complete two-loop calculation in a scalar-Yukawa model.

Extended the calculation to a novel three-loop level without high-temperature approximations.

Demonstrated the method's potential for precise predictions in models with strong first-order phase transitions.

Abstract

We introduce a new framework for perturbatively computing equilibrium thermodynamic properties of cosmological phase transitions to high loop orders, using the full four-dimensional resummed thermal effective potential and avoiding the limitations of standard high-temperature approximations. By systematically disentangling the physics of hard and soft momentum scales, our approach unifies their treatment within a single expression, enabling consistent handling of both vacuum and thermal divergences across all mass regimes. This core innovation enables the efficient numerical evaluation of massive multiloop thermal sum-integrals, achieved through a finite-temperature generalization of Loop-Tree Duality -- an advanced algorithmic technique originally developed to render vacuum Feynman integrals numerically tractable via Monte Carlo methods. As a proof of principle, we apply the framework to a scalar-Yukawa model, presenting a complete two-loop calculation and a novel three-loop extension -- the first fully massive three-loop sum-integral computation without relying on high-temperature expansions. Our approach opens the door to precise perturbative predictions of the phase structure in a broad class of beyond-the-Standard-Model scenarios, including those featuring strong first-order phase transitions relevant for gravitational-wave signals, where conventional high-temperature approximations break down.