  We investigate the effects of a large-scale background hypermagnetic field on
the electroweak phase transition. We propose a model in which an effective weak
angle varies during the electroweak phase transition and upon its use we show
that, although for the majority of the parameter space the phase transition is
a crossover, there are tiny regions in which the phase transition occurs in two
steps and can be first-order. We obtain all of the important quantities
characterizing the details of the first-order phase transition, including the
latent heat, transition temperature and duration. We then calculate the
gravitational wave energy spectrum generated during the first-order part of the
electroweak phase transition and find that, for strong enough background
hypermagnetic fields, these signals can be detected by the Ultimate-DECIGO
interferometer.
