Generation of magnetic fields and gravitational waves at neutrino decoupling

We show that an inhomogeneous cosmological lepton number may have produced turbulence in the primordial plasma when neutrinos entered the (almost) free-streaming regime. This effect may be responsible for the origin of cosmic magnetic fields and give rise to a detectable background of gravitational waves. An existence of inhomogeneous lepton asymmetry could be naturally generated by active-sterile neutrino oscillations or by some versions of the Affleck-Dine baryogenesis scenario.