Constraints on the strength of a primordial magnetic field from big bang nucleosynthesis

The effects of magnetic fields on big bang nucleosynthesis (BBN) are calculated, and the impact on the abundances of the light elements are investigated numerically. An upper limit on the strength of primordial magnetic fields compatible with observations of light element abundances is thus obtained. In the framework of standard BBN theory, the maximum strength of the primordial magnetic fields, on scales greater than ${10}^4$ cm but smaller than the event horizon at the BBN epoch (∼1 min, ∼2×${10}^{12}$ cm), is ≤${10}^{11}$ G. This limit is shown to allow magnetic fields at the time of recombination no stronger than ∼0.1 G on scales ≥${10}^{11}$ cm. Our results also strongly indicate that, at the BBN epoch, and for field strengths $B\le {10}^{13}$ G, the effects of magnetic fields on the primordial abundances of light elements are dominated by effects from reaction rates in the presence of primeval magnetic fields rather than by magnetic density effects on the expansion rate.