Dirac Neutrinos and Primordial Magnetic Fields

We consider random primordial magnetic fields and discuss their dissipation, coherence length $L_0$, scaling behaviour and constraints implied by the primoridal nucleosynthesis. Such magnetic fields could excite the right-helicity states of Dirac neutrinos, with adverse consequences for nucleosynthesis. We present solutions to the spin kinetic equation of a Dirac neutrino traversing a random magnetic field in the cases of large and small $L_0$, taking also into account elastic collisions. Depending on the scaling behaviour and on the magnetic coherence length, the lower limit on the neutrino magnetic moment thus obtained could be as severe as $10^{-20}\mu_B$.