Bubble nucleation of spatial vector fields

Abstract

We study domain walls and bubble nucleation in a nonrelativistic vector field theory with different longitudinal and transverse speeds of sound. We describe analytical and numerical methods to calculate the orientation-dependent domain-wall tension $\ensuremath{\sigma}(\ensuremath{\theta})$. We then use this tension to calculate the critical bubble shape and show that the tunneling exponent is modified by a factor of sound speed ratio. This implies a big modification in the tunneling rate. The longitudinally oriented domain wall tends to be the heaviest and sometime suffers an instability. It can spontaneously break into zigzag segments. In this case, the critical bubble develops kinks, and its energy, and therefore the tunneling rate, scales with the sound speeds very differently than what would be expected for a smooth bubble.