  We point out that the transition probabilities used in a recent perturbative
calculation of pair creation in an external magnetic field in the expanding de
Sitter space with the $in$ and $out$ fermion states defined by the Bunch-Davies
modes [C. Crucean et al., Phys. Rev. D 73 044019 (20016)] are gauge dependent
quantities. We examine the gauge variations of these amplitudes assuming a
decoupling of the interaction at infinite times, which allows to conclude that
the source of the problem lies in the nonoscillatory behavior of the fermion
current in the infinite future.
