Neutrino-electron magnetohydrodynamics in an expanding Universe
  We derive a new model for neutrino-plasma interactions in an expanding
universe that incorporates the collective effects of the neutrinos on the
plasma constituents. We start from the kinetic description of a multi-species
plasma in the flat Friedmann-Robertson-Walker metric, where the particles are
coupled to neutrinos through the charged- and neutral-current forms of the weak
interaction. We then derive the fluid equations and specialize our model to (a)
the lepton epoch, where we consider a pair electron-positron plasma interacting
with electron (anti-)neutrinos, and (b) after the electron-positron
annihilation, where we model an electron-proton plasma and take the limit of
slow ions and inertia-less electrons to obtain a set of neutrino-electron
magnetohydrodynamics (NEMHD) equations. In both models, the dynamics of the
plasma is affected by the neutrino motion through a ponderomotive force and, as
a result, new terms appear in the induction equation that can act as a source
for magnetic field generation in the early universe. A brief discussion on the
possible applications of our model is proposed.
