Higher-order corrections to the bubble-nucleation rate at finite temperature

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 main goal of this paper is to investigate the convergence and uncertainty of all calculation. Doing so I argue that current calculations for the Standard Model with a tree-level barrier are inaccurate.