Abstract
We study the generation of magnetic field seeds during a first-order electroweak phase transition, by numerically evolving the classical equations of motion of the bosonic electroweak theory on the lattice. The onset of the transition is implemented by the random nucleation of bubbles with an arbitrarily oriented Higgs field in the broken phase. We find that about 10% of the latent heat is converted into magnetic energy, with most of the magnetic fields being generated in the last stage of the phase transition when the Higgs oscillates around the true vacuum. The energy spectrum of the magnetic field has a peak that shifts towards larger length scales as the phase transition unfolds. By the end of our runs the peak wavelength is of the order of the bubble percolation scale, or about a third of our lattice size.
Highlights
Magnetic fields are pervasive in the Universe
V we allow for bubbles to nucleate at random locations in the unbroken phase and we present the spectrum of the magnetic field induced during a first-order electroweak phase transition (EWPT)
We have simulated the classical dynamics of the bosonic electroweak theory to study the generation of magnetic fields during the EWPT, assuming that physics beyond the Standard Model (SM) yields a first-order transition
Summary
Magnetic fields are pervasive in the Universe. Microgauss fields coherent on scales up to ten kpc have been detected in nearby spiral galaxies, such as the Milky Way and in higher redshift galaxies (e.g., [1]). A cosmological first-order phase transition can be a source of gravitational waves (GWs) [35,36] In this respect, largescale numerical simulations of a scalar field theory on the lattice have recently become available to verify the production of GW radiation during a first-order phase transition [37,38,39]. Largescale numerical simulations of a scalar field theory on the lattice have recently become available to verify the production of GW radiation during a first-order phase transition [37,38,39] Our results bring another handle to probe the universe at the time of the EWPT: the observation of cosmological magnetic fields.
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