Helical magnetic fields via baryon asymmetry

There is strong observational evidence for the presence of large-scale magnetic fields MF in galaxies and clusters, with strength $\sim \mu$G and coherence lenght on the order of Kpc. However its origin remains as an outstanding problem. One of the possible explanations is that they have been generated in the early universe. Recently, it has been proposed that helical primordial magnetic fields PMFs, could be generated during the EW or QCD phase transitions, parity-violating processes and predicted by GUT or string theory. Here we concentrate on the study of two mechanisms to generate PMFs, the first one is the $\nu$MSM which triggers instability in the Maxwell's equations and leads to the generation of helical PMFs. The second one is the usual electroweak baryogenesis scenario. Finally, we calculate the exact power spectra of these helical PMFs and we show its role in the production of gravitational waves finding a scale-invariant on large scales and an oscillatory motion (damping) for $k\eta \gg 1$