Massive neutrinos, helium production and the primordial magnetic field

Experimental evidence¹ for a non-zero neutrino rest mass, m _v≠0, while still controversial², poses intriguing cosmological questions^3-10. One reassurance is that the possibility of non-zero masses does not necessarily alter previous predictions of the standard big-bang model for the primordial ⁴He abundance, Y. We show here that a non-zero neutrino rest mass, m_v ∼ 10eV, may provide the most stringent upper limit proposed to date on the strength of any ordered, primordial magnetic field: B₀≲4 × 10^-9/m _v (eV) G. This limit is set by requiring that previous predictions of the standard big bang model for the primordial ⁴He abundance remain unaltered by the spin procession and subsequent thermalization of right-handed, as well as left-handed, Dirac neutrinos in the early Universe.