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