Abstract
Assuming that the electroweak and QCD phase transitions are first order, upon supercooling, bubbles of the new phase appear. These bubbles grow to macroscopic sizes compared to the natural scales associated with the Compton wavelengths of particle excitations. They propagate by burning the old phase into the new phase at the surface of the bubble. We study the hydrodynamic stability of the burning and find that for the velocities of interest for cosmology in the electroweak phase transition, the shape of the bubble wall is stable under hydrodynamic perturbations. Bubbles formed in the cosmological QCD phase transition are found to be a borderline case between stability and instability.
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