HELICAL MAGNETIC FIELDS FROM INFLATION

We analyze the generation of seed magnetic fields during de Sitter inflation considering a noninvariant conformal term in the electromagnetic Lagrangian of the form - 1/4I(phi)F-mu nu(F) over tilde (mu nu) where I(phi) is a pseudoscalar function of a nontrivial background field phi. In particular, we consider a toy model that could be realized owing to the coupling between the photon and either a (tachyonic) massive pseudoscalar field or a massless pseudoscalar field nonminimally coupled to gravity, where I follows a simple power law behavior I(k, eta) = g/(-k eta)(beta) during inflation, while it is negligibly small subsequently. Here, g is a positive dimensionless constant, k the wave number, eta the conformal time, and beta a real positive number. We find that only when beta = 1 and 0.1 less than or similar to g less than or similar to 2 can astrophysically interesting fields be produced as excitation of the vacuum, and that they are maximally helical.