Generation of helical magnetic field in a viable scenario of inflationary magnetogenesis

We study the generation of helical magnetic fields in a model of inflationary magnetogenesis which is free from the strong coupling and backreaction problems. To generate helical magnetic fields, we add an f2F˜μνFμν term to the Lagrangian of the Ratra model. The strong coupling and backreaction problems are avoided if we take a particular behavior of coupling function f, in which f increases during inflation and decreases postinflation to reheating. The generated magnetic field is fully helical and has a blue spectrum, dρB/dlnk∝k4. This spectrum is obtained when coupling function f∝a2 during inflation. The scale of reheating in our model has to be lower than 4000 GeV to avoid backreaction postinflation. The generated magnetic field spectrum satisfies the γ-ray bound for all the possible scales of reheating. The comoving magnetic field strength and its correlation length are ∼4×10−11 G and 70 kpc respectively, if reheating takes place at 100 GeV. For reheating at the QCD scales of 150 MeV, the field strength increases to ∼ nano gauss, with coherence scale of 0.6 Mpc.