Cosmological bubble friction in local equilibrium

Abstract

In first-order cosmological phase transitions, the asymptotic velocity of expanding bubbles is of crucial relevance for predicting observables like the spectrum of stochastic gravitational waves, or for establishing the viability of mechanisms explaining fundamental properties of the universe such as the observed baryon asymmetry. In these dynamic phase transitions, it is generally accepted that subluminal bubble expansion requires out-of-equilibrium interactions with the plasma which are captured by friction terms in the equations of motion for the scalar field. We show that subluminal propagation can still happen in the case of local equilibrium, in which the total entropy remains conserved but bubbles slow down due to hydrodynamic effects across the bubble wall associated with the field-dependence of the entropy density. These effects can by accounted for by simply imposing local conservation of stress-energy and including field dependent thermal contributions to the effective potential. We illustrate this with explicit calculations of dynamical and static bubbles for a first-order electroweak transition in a Standard Model extension with additional scalar fields. The results qualitatively match with recent analyses of friction forces in local equilibrium, which discard runaway behaviours, although we find corrections from the temperature and velocity gradients across the bubble. Even if local equilibrium is violated for some particle species, the effects described here will apply for the background plasma of the species that remain equilibrated, thereby leading to smaller velocities.