Is inflationary magnetogenesis sensitive to the post-inflationary history ?

Considering inflationary magnetogenesis induced by time-dependent kinetic and axial couplings of a massless Abelian vector boson field breaking the conformal invariance we show in this article that, surprisingly, the spectral shape of the large-scale primordial magnetic field power spectrum is insensitive to the post-inflationary history, namely the barotropic parameter ($w$) and the gauge coupling functions of the post-inflationary era.