  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.
