Magnetic moment of massive neutrinos and the cosmic helium abundances

We point out that if neutrinos have mass they will also develop a magnetic dipole moment. We calculate that moment in the simplest extension of the Weinberg-Salam theory. We then propose that spin precession in the magnetic fields of the early universe may be an important production mechanism for right-handed neutrinos from life-handed neutrinos. We consider two models of the primordial magnetic field—one based on the equipartition of energy and the other a "flux-freezing" model—and show that the angle of spin precession can be large. Since we would expect very different cosmic abundances of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at present if right-handed neutrinos were to come into thermal equilibrium before the onset of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ production, we are thus able to put a constraint on the amount of spin precession of neutrinos in the early universe. This, in turn, allows us to set severe constraints on either the mass of each light neutrino in the $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ model, on the magnetic moment in an arbitrary model, or on the magnitude of any intergalactic magnetic field which is a remnant of the early universe.