The 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 back-reaction problems. To generate helical magnetic fields, we add an $f^2{\tilde{F}}^{\mu \nu }{F}_{\mu \nu }$ term to the lagrangian of Ratra model. The strong coupling and back-reaction problems are avoided if we take a particular behaviour of coupling function $f$, in which $f$ increases during inflation and decreases post inflation to reheating. The generated magnetic field is fully helical and has a blue spectrum, $d{\rho }_B/d\ln k\propto k^4$. This spectrum is obtained when coupling function $f\propto a^2$ during inflation. The scale of reheating in our model has to be lower than $4000$ GeV to avoid back-reaction post inflation. The generated magnetic field spectrum satisfies the $\gamma$-ray bound for all the possible scales of reheating. The comoving magnetic field strength and its correlation length are $\sim 4\times 10^{-11}$ 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 $\sim$ nano gauss, with coherence scale of $0.6$ Mpc.

arXiv comment11 pages, Submitted to PRD

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