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

Abstract

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 ${f}^{2}{\stackrel{\texttildelow{}}{F}}^{\ensuremath{\mu}\ensuremath{\nu}}{F}_{\ensuremath{\mu}\ensuremath{\nu}}$ 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, $d{\ensuremath{\rho}}_{B}/d\mathrm{ln}k\ensuremath{\propto}{k}^{4}$. This spectrum is obtained when coupling function $f\ensuremath{\propto}{a}^{2}$ 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 $\ensuremath{\gamma}$-ray bound for all the possible scales of reheating. The comoving magnetic field strength and its correlation length are $\ensuremath{\sim}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\text{ }\text{ }\mathrm{G}$ 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 $\ensuremath{\sim}$ nano gauss, with coherence scale of 0.6 Mpc.