WallGo investigates: Theoretical uncertainties in the bubble wall velocity

Abstract

We examine theoretical uncertainties in state-of-the-art calculations of the bubble wall velocity during first-order cosmological phase transitions. By utilising the software WallGo for two extensions of the Standard Model, we find several $O(1)$ uncertainties arising from the number of particles taken out of equilibrium, the logarithmically and power enhanced collision integrals, the treatment of thermal masses, the nucleation temperature, the $\tanh$ ansatz, and the perturbative order of the effective potential. However, we show that the linearisation of the Boltzmann equations is generally a good approximation with much smaller associated errors. We further clarify the limitations of the quasiparticle approximation in regions with negative mass squared. This study provides a detailed uncertainty budget and highlights where future efforts should be directed to improve the reliability of wall velocity and hence gravitational wave predictions.