Friction forces on phase transition fronts

In cosmological first-order phase transitions, the microscopic interaction of the phase transition fronts with non-equilibrium plasma particles manifests itself macroscopically as friction forces. In general, it is a nontrivial problem to compute these forces, and only two limits have been studied, namely, that of very slow walls and, more recently, ultra-relativistic walls which run away. In this paper we consider ultra-relativistic velocities and show that stationary solutions still exist when the parameters allow the existence of runaway walls. Hence, we discuss the necessary and sufficient conditions for the fronts to actually run away. We also propose a phenomenological model for the friction, which interpolates between the non-relativistic and ultra-relativistic values. Thus, the friction depends on two friction coefficients which can be calculated for specific models. We then study the velocity of phase transition fronts as a function of the friction parameters, the thermodynamic parameters, and the amount of supercooling.Comment: 34 pages, 7 figures. v2: minor correction

Hydrodynamics of phase transition fronts and the speed of sound in the plasma

The growth of bubbles in cosmological first-order phase transitions involves nontrivial hydrodynamics. For that reason, the study of the propagation of phase transition fronts often requires several approximations. A frequently used approximation consists in describing the two phases as being composed only of radiation and vacuum energy (the so-called bag equation of state). We show that, in realistic models, the speed of sound in the low-temperature phase is generally smaller than that of radiation, and we study the hydrodynamics in such a situation. We find in particular that a new kind of hydrodynamical solution may be possible, which does not arise in the bag model. We obtain analytic results for the efficiency of the transfer of latent heat to bulk motions of the plasma, as a function of the speed of sound in each phase.Comment: 44 pages, 19 figures. v2: some comments and references added. v3: Some discussions and a figure added. Results unchanged. Matches published versio

Gravitational waves from a very strong electroweak phase transition

We investigate the production of a stochastic background of gravitational waves in the electroweak phase transition. We consider extensions of the Standard Model which can give very strongly first-order phase transitions, such that the transition fronts either propagate as detonations or run away. To compute the bubble wall velocity, we estimate the friction with the plasma and take into account the hydrodynamics. We track the development of the phase transition up to the percolation time, and we calculate the gravitational wave spectrum generated by bubble collisions, magnetohydrodynamic turbulence, and sound waves. For the kinds of models we consider, we find parameter regions for which the gravitational waves are potentially observable at the planned space-based interferometer eLISA. In such cases, the signal from sound waves is generally dominant, while that from bubble collisions is the least significant of them. Since the sound waves and turbulence mechanisms are diminished for runaway walls, the models with the best prospects of detection at eLISA are those which do not have such solutions. In particular, we find that heavy extra bosons provide stronger gravitational wave signals than tree-level terms.Comment: 30 pages, 12 figures. v2: typos corrected, explanations improved, a figure and a few references added. v3: comments added; matches JCAP versio

Stability of cosmological deflagration fronts

In a cosmological first-order phase transition, bubbles of the stable phase nucleate and expand in the supercooled metastable phase. In many cases, the growth of bubbles reaches a stationary state, with bubble walls propagating as detonations or deflagrations. However, these hydrodynamical solutions may be unstable under corrugation of the interface. Such instability may drastically alter some of the cosmological consequences of the phase transition. Here, we study the hydrodynamical stability of deflagration fronts. We improve upon previous studies by making a more careful and detailed analysis. In particular, we take into account the fact that the equation of motion for the phase interface depends separately on the temperature and fluid velocity on each side of the wall. Fluid variables on each side of the wall are similar for weakly first-order phase transitions, but differ significantly for stronger phase transitions. As a consequence, we find that, for large enough supercooling, any subsonic wall velocity becomes unstable. Moreover, as the velocity approaches the speed of sound, perturbations become unstable on all wavelengths. For smaller supercooling and small wall velocities, our results agree with those of previous works. Essentially, perturbations on large wavelengths are unstable, unless the wall velocity is higher than a critical value. We also find a previously unobserved range of marginally unstable wavelengths. We analyze the dynamical relevance of the instabilities, and we estimate the characteristic time and length scales associated to their growth. We discuss the implications for the electroweak phase transition and its cosmological consequences.Comment: 45 pages, 13 figures. v2: Minor corrections, references added. v3: Typos corrected, minor modifications and references added (version accepted in PRD

Hydrodynamics of ultra-relativistic bubble walls

In cosmological first-order phase transitions, gravitational waves are generated by the collisions of bubble walls and by the bulk motions caused in the fluid. A sizeable signal may result from fast-moving walls. In this work we study the hydrodynamics associated to the fastest propagation modes, namely, ultra-relativistic detonations and runaway solutions. We compute the energy injected by the phase transition into the fluid and the energy which accumulates in the bubble walls. We provide analytic approximations and fits as functions of the net force acting on the wall, which can be readily evaluated for specific models. We also study the back-reaction of hydrodynamics on the wall motion, and we discuss the extrapolation of the friction force away from the ultra-relativistic limit. We use these results to estimate the gravitational wave signal from detonations and runaway walls.Comment: 30 pages, 11 figures. v2: typos corrected, reference added, a new fit provided in the appendix. v3: a section on GWs added; matches version accepted in NP

Stability of cosmological detonation fronts

The steady state propagation of a phase transition front is classified, according to hydrodynamics, as a deflagration or a detonation, depending on its velocity with respect to the fluid. These propagation modes are further divided into three types, namely, weak, Jouguet, and strong solutions, according to their disturbance of the fluid. However, some of these hydrodynamic modes will not be realized in a phase transition. One particular cause is the presence of instabilities. In this work we study the linear stability of weak detonations, which are generally believed to be stable. After discussing in detail the weak detonation solution, we consider small perturbations of the interface and the fluid configuration. When the balance between the driving and friction forces is taken into account, it turns out that there are actually two different kinds of weak detonations, which behave very differently as functions of the parameters. We show that the branch of stronger weak detonations are unstable, except very close to the Jouguet point, where our approach breaks down.Comment: 34 pages, 11 figures. v2: typos corrected and minor change

Analytic approach to the motion of cosmological phase transition fronts

We consider the motion of planar phase-transition fronts in first-order phase transitions of the Universe. We find the steady state wall velocity as a function of a friction coefficient and thermodynamical parameters, taking into account the different hydrodynamic modes of propagation. We obtain analytical approximations for the velocity by using the thin wall approximation and the bag equation of state. We compare our results to those of numerical calculations and discuss the range of validity of the approximations. We analyze the structure of the stationary solutions. Multiple solutions may exist for a given set of parameters, even after discarding non-physical ones. We discuss which of these will be realized in the phase transition as the stationary wall velocity. Finally, we discuss on the saturation of the friction at ultra-relativistic velocities and the existence of runaway solutions.Comment: 25 pages, 9 figures. The title has changed. A discussion on the saturation of the friction and the possibility of runaway walls has been adde

Strings With Axionic Content and Baryogenesis

We describe different electroweak strings with axionic content, including non-topological configurations calculated numerically, and show their possible influence on baryogenesis indicating that they may constitute a mechanism competitive to that of bubble nucleation with two Higgs-doublets.Comment: 12 page