Primordial magnetic seed field amplification by gravitational waves: comment on gr-qc/0503006

The potential amplification of primordial seed magnetic fields by gravitational waves was discussed in [1], wherein a mechanism was proposed and an amplification of several orders of magnitude was obtained. Recently, this mechanism was revisited in [2] and the original results were recovered both qualitatively and quantitatively. Despite this, the comparison of the two papers is misleading and reaches erroneous conclusions that need to be clarified. Relatively recently, a scenario for the amplification of primordial, inflation produced magnetic seeds through gravitational wave interactions was proposed in the literature [1]. The mechanism operates soon after inflation and within standard electromagnetic theory. This purely gravitational strengthening of the initial field can be quite substantial when the two sources have comparable wavelengths (see [1] for details). The main results of [1] are given in Eqs. (21) and (25). These are summarised in the expression (see Eq. (26) in [1]) B ρ 1/2 γ ≃ [ 1 + 10 ( λB̃ λH 2 0 ( σ H )