Magnetic Field and Gravitational Waves from the First-Order Phase Transition

We perform the three-dimensional lattice simulation of the magnetic field and gravitational wave productions from bubble collisions during the first-order electroweak phase transition. Except for the gravitational wave, the power-law spectrum of the magnetic field strength is numerically calculated for the first time, which is of a broken power-law spectrum: B-xi proportional to f(0.)(91) for the low-frequency region of f < f(*) and B-xi proportional to f(-1.65) for the high-frequency region of f > f(*) in the thin-wall limit, with the peak frequency being f(*) similar to 5 Hz at the phase transition temperature 100 GeV. When the hydrodynamics is taken into account, the generated magnetic field strength can reach B-xi similar to 10(-7 )G at a correlation length xi similar to 10(-7) pc, which may seed the large scale magnetic fields. Our study shows that the measurements of cosmic magnetic field strength and gravitational waves are complementary to probe new physics admitting electroweak phase transition.