Primordial magnetic fields from preheating at the electroweak scale
  We analyze the generation of helical magnetic fields during preheating in a model of low-scale electroweak (EW) hybrid inflation. We show how the inhomogeneities in the Higgs field, resulting from tachyonic preheating after inflation, seed the magnetic fields in a way analogous to that predicted by Vachaspati and Cornwall in the context of the EW symmetry breaking. At this stage, the helical nature of the generated magnetic fields is linked to the non-trivial winding of the Higgs-field. We analyze non-perturbatively the evolution of these helical seeds through the highly non-linear stages of symmetry breaking (SB) and beyond. Electroweak SB occurs via the nucleation and growth of Higgs bubbles which squeeze the magnetic fields into string-like structures. The W-boson charge density clusters in lumps around the magnetic strings. After symmetry breaking, a detailed analysis of the magnetic field Fourier spectrum shows two well differentiated components: a UV radiation tail at a temperature T ~ 0.23 m_higgs slowly growing with time, and an IR peak associated to the helical magnetic fields, which seems to follow inverse cascade. The system enters a regime in which we observe that both the amplitude (\rho_B/\rho_{EW} ~ 0.01) and the correlation length of the magnetic field grow linearly with time. During this stage of evolution we also observe a power-law growth in the helical susceptibility. These properties support the possibility that our scenario could provide the seeds eventually evolving into the microgauss fields observed today in galaxies and clusters of galaxies. 
Andres Diaz-Gil, Juan Garcia-Bellido, Margarita Garcia Perez and   Antonio Gonzalez-Arroyo