Stability of cosmological deflagration fronts

Abstract

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

Detecting gravitational waves from cosmological phase transitions with LISA: an update

“…Ab initio calculations of this friction is in many models still lacking. The stability of the bubble wall front is also a topic that is debated in the literature [199][200][201][202][203][204][205][206][207][208][209]. Additionally, there remain several open questions regarding perturbative calculations of the PT parameters.…”

Numerical simulations of acoustically generated gravitational waves at a first order phase transition

“…We noted that we need larger simulations to trace out the shape of the power spectrum at wavenumbers lower than the peak value, and to determine the index of the power spectrum for the transitions with faster bubble walls. They may also help in the search for bubble wall instabilities identified in [57][58][59]. We also need to develop a theoretical understanding of the shape or the power spectrum, and most importantly making accurate quantitative predictions for future gravitational wave observatories.…”

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“…5 Recent years have seen progress in matching models onto these existing results [54,[80][81][82] and in the hydrodynamic considerations associated with bubble wall expansion (see e.g. [83][84][85][86][87][88][89]). …”