Bounds on the bubble wall velocity

TL;DR

This paper establishes bounds on the velocity of bubble walls during first-order phase transitions, independent of collision term uncertainties, by analyzing local thermal equilibrium and ballistic limits, with implications for cosmological models.

Contribution

It derives model-independent bounds on bubble wall velocity, incorporating plasma inhomogeneities and testing them within the singlet extended Standard Model.

Findings

Bounds are independent of collision term uncertainties.

Hydrodynamic obstruction exists in both equilibrium and ballistic limits.

Ballistic approximation requires accounting for plasma inhomogeneities.

Abstract

Determining the bubble wall velocity in first-order phase transitions is a challenging task, requiring the solution of (coupled) equations of motion for the scalar field and Boltzmann equations for the particles in the plasma. The collision terms appearing in the Boltzmann equation present a prominent source of uncertainty as they are often known only at leading log accuracy. In this paper, we derive upper and lower bounds on the wall velocity, corresponding to the local thermal equilibrium and ballistic limits. These bounds are completely independent of the collision terms. For the ballistic approximation, we argue that the inhomogeneous plasma temperature and velocity distributions across the bubble wall should be taken into account. This way, the hydrodynamic obstruction previously observed in local thermal equilibrium is also present for the ballistic approximation. This is essential for the ballistic approximation to provide a lower bound on the wall velocity. We use a model-independent approach to study the behaviour of the limiting wall velocities as a function of a few generic parameters, and we test our developments in the singlet extended Standard Model.