Comment on “Constraints on the strength of primordial magnetic fields from big bang nucleosynthesis reexamined”

Recently Cheng, Olinto, Schramm, and Truran reexamined the constraints on the strength of primordial $B$ fields from big bang nucleosynthesis (BBN). Their bottom line agreed with that of an earlier recent paper on the subject by Kernan, Starkman, and Vachaspati, both in its final limit on the $B$ field during BBN and in its conclusion that, for allowed values of the $B$ field, the dominant factor for BBN is the increased expansion rate at a given temperature caused by the energy density of the magnetic field, $B^2/8\mathrm{}\pi$. However, their conclusion that weak interaction rates increased with an increasing $B$ field at these low field values contradicted the earlier results of Kernan, Starkman, and Vachaspati. In this Comment we point out that the Taylor series expansion of the weak interaction rate about $B=0\mathrm{}$ used by Cheng et al. is not well defined, while the Euler-McLaurin expansion of Kernan, Starkman, and Vachaspati is well behaved and reliable. Using the Euler-McLaurin expansion we find that the weak interaction rates decrease rather than increase with an increasing $B$ field at small values of the $B$ field.