Instability of cosmological magnetic fields in electroweak plasma driven by neutrino asymmetries

The magnetohydrodynamics (MHD) is modified to incorporate the parity violation in the Standard Model leading to a new instability of magnetic fields in the electroweak plasma in the presence of nonzero neutrino asymmetries. The main ingredient for such a modified MHD is the antisymmetric part of the photon polarization tensor in plasma, where the parity violating neutrino interaction with charged leptons is present. The growth of a cosmological magnetic field driven by the neutrino asymmetry density $\Delta n_{\nu}= n_{\nu} - n_{\bar{\nu}\neq 0}$ is provided by a lower bound on neutrino asymmetry $\mid\xi_{\nu_e}\mid=\mu_{\nu_e}/T$, where $\mu_{\nu_e}$ is the neutrino chemical potential, $T$ is the plasma temperature, which is consistent with the well-known Big Bang nucleosynthesis (upper) bound on electron neutrino asymmetry in a hot universe plasma.