Inflationary helical magnetic fields with a sawtooth coupling

TL;DR

This paper presents a model for generating helical magnetic fields during inflation that avoids strong coupling issues, producing fields consistent with observational bounds and with larger coherence lengths due to magneto-hydrodynamical evolution.

Contribution

The study introduces a novel inflationary model with a sharp transition in coupling, successfully generating observable helical magnetic fields without strong coupling or back-reaction problems.

Findings

Generated magnetic fields match intergalactic bounds from blazar data.

The model produces scale-invariant spectra up to the transition.

Magneto-hydrodynamical evolution increases coherence lengths significantly.

Abstract

We study the generation of helical magnetic fields during inflation by considering a model which does not suffer from strong coupling or large back-reaction. Electromagnetic conformal invariance is broken only during inflation by coupling the gauge-invariants $F_{\mu\nu}F^{\mu\nu}$ and $F_{\mu\nu}{\tilde{F}}^{\mu\nu}$ to a time-dependent function $I$ with a sharp transition during inflation. The magnetic power spectrum is scale-invariant up to the transition and very blue-shifted after that. The subsequent evolution of the helical magnetic field is subjected to magneto-hydrodynamical processes, resulting in far larger coherence lengths than those occurring after adiabatic decay. Scale-invariant quadratic gravity is a suitable framework to test the model, providing a natural physical interpretation. We show that fully helical magnetic fields are generated with values in agreement with the lower bounds on fields in the Intergalactic Medium derived from blazar observations. This model holds even at large/intermediate energy scales of inflation, contrary to what has been found in previous works.