Inflation-Produced Magnetic Fields in R^n F^2 and I F^2 models

We re-analyze the production of seed magnetic fields during Inflation in (R/m^2)^n F_{\mu \nu}F^{\mu \nu} and I F_{\mu \nu}F^{\mu \nu} models, where n is a positive integer, R the Ricci scalar, m a mass parameter, and I \propto \eta^\alpha a power-law function of the conformal time \eta, with \alpha a positive real number. If m is the electron mass, the produced fields are uninterestingly small for all n. Taking m as a free parameter we find that, for n \geq 2, the produced magnetic fields can be sufficiently strong in order to seed dynamo mechanism and then to explain galactic magnetism. For \alpha \gtrsim 2, there is always a window in the parameters defining Inflation such that the generated magnetic fields are astrophysically interesting. Moreover, if Inflation is (almost) de Sitter and the produced fields almost scale-invariant (\alpha \simeq 4), their intensity can be strong enough to directly explain the presence of microgauss galactic magnetic fields.