We reanalyze 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 $n\ge 2$, the produced magnetic fields can be sufficiently strong in order to seed the 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.

• Received 14 March 2008

DOI:https://doi.org/10.1103/PhysRevD.77.123002