Hypermagnetic Knots, Chern-Simons Waves and the Baryon Asymmetry

At finite hyperconductivity and finite fermionic density the flux lines of long range hypermagnetic fields may not have a topologically trivial structure. The combined evolution of the chemical potentials and of pseudoscalar fields (like the axial Higgs), possibly present for temperatures in the TeV range, can twist the hypercharge flux lines, producing, ultimately, hypermagnetic knots (HK). The dynamical features of the HK depend upon the various particle physics parameters of the model (pseudoscalar masses and couplings, strength of the electroweak phase transition, hyperconductivity of the plasma) and upon the magnitude of the primordial flux sitting in topologically trivial configurations of the hypermagnetic field. We study different cosmological scenarios where HK can be generated. We argue that the fermionic number sitting in HK can be released producing a seed for the Baryon Asymmetry of the Universe (BAU) provided the typical scale of the knot is larger than the diffusivity length scale. We derive constraints on the primordial hypermagnetic flux required by our mechanism and we provide a measure of the parity breaking by connecting the degree of knottedness of the flux lines to the BAU. We rule out the ordinary axion as a possible candidate for production (around temperatures of the order of the GeV) of {\em magnetic} knots since the produced {\em electromagnetic} helicity is negligible (for cosmological standard) if the initial amplitude of the axion oscillations is of the order of the Peccei-Quinn breaking scale.