Big bang nucleosynthesis constraints on primordial magnetic fields

We reanalyze the effect of magnetic fields in BBN, incorporating several features which were omitted in previous analyses. We find that the effects of coherent magnetic fields on the weak interaction rates and the electron thermodynamic functions (${\rho }_e$, $P_e$, and $\frac{d{\rho }_e}{d{T}_{\gamma }}$) are unimportant in comparison with the contribution of the magnetic field energy density in BBN. As a consequence the effect of including magnetic fields in BBN is well approximated numerically by treating the additional energy density as an effective neutrino number. A conservative upper bound on the primordial magnetic field, parametrized as $\zeta =\frac{2e{B}_{\mathrm{rms}}}{\left(T_{\nu }^2\right)}$, is $\zeta <~2({\rho }_B<0.27\mathrm{}{\rho }_{\nu })$. This bound can be stronger than the conventional bound coming from the Faraday rotation measures of distant quasars if the cosmological magnetic field is generated by a causal mechanism.