Inflationary helical magnetic fields with a sawtooth coupling

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.