**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 analyse 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.

**Author affiliation**: Membiela, Federico Agustin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata; Argentina

**Author affiliation**: Megevand, Ariel Hugo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata; Argentina