Higher-Order Corrections to the Bubble-Nucleation Rate at Finite Temperature

TL;DR

This paper develops and compares methods for accurately calculating bubble-nucleation rates at finite temperature, reducing uncertainties crucial for gravitational-wave predictions in cosmology.

Contribution

It introduces a consistent approach to include higher-order corrections in bubble-nucleation rate calculations and compares different computational methods for improved accuracy.

Findings

Derivative expansion's applicability is analyzed.

Numerical Gelfand-Yaglom method is validated against the derivative expansion.

Higher-order corrections significantly impact Standard Model bubble-nucleation estimates.

Abstract

In this paper I discuss how to consistently incorporate higher-order corrections to the bubble-nucleation rate at finite temperature. Doing so I examine the merits of different approaches, with the goal of reducing uncertainties for gravitational-wave calculations. To be specific, the region of applicability and accuracy of the derivative expansion is discussed. The derivative expansion is then compared to a numerical implementation of the Gelfand-Yaglom theorem. Both methods are applied to popular first-order phase transition models, like a loop-induced barrier and a SM-EFT tree-level barrier. The results of these calculations are presented in easy-to-use parametrizations that can directly be used in gravitational-wave calculations. In addition, higher-order corrections for models with multiple scalar fields, such as singlet/triplet extensions, are studied. Lastly, the convergence and uncertainty of all calculations are discussed in detail. And I argue that leading-order results for the Standard Model with a tree-level barrier might be inaccurate.