We investigate the effects of a large-scale background hypermagnetic field on
the electroweak phase transition. We propose an effective weak angle which
varies during the electroweak phase transition and upon its use, show that for
a strong enough hypermagnetic field the phase transition occurs in two steps
and becomes first-order. We obtain all of the important quantities
characterizing the details of the phase transition, including the latent heat,
transition temperature and duration. We then explore one of the consequences of
this model which is the generation of gravitational waves. We calculate the
gravitational wave energy spectrum generated during the first-order electroweak
phase transition and find that, for strong enough background hypermagnetic
fields, these signals can be detected by the Ultimate-DECIGO interferometer.Comment: 19 pages, 7 figures; v3: more discussions adde