The generation of helical magnetic field in a viable scenario of Inflationary Magnetogenesis

TL;DR

This paper proposes a viable inflationary magnetogenesis model that generates fully helical magnetic fields with a blue spectrum, avoiding strong coupling and back-reaction issues, and consistent with observational bounds across various reheating scales.

Contribution

It introduces a modified coupling function in the Ratra model to produce helical magnetic fields during inflation without the usual problems, and analyzes the resulting spectrum and observational constraints.

Findings

Generated magnetic fields are fully helical with a blue spectrum.

The model's magnetic field strength and coherence length depend on the reheating scale.

The spectrum satisfies gamma-ray bounds for all reheating scenarios.

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.