Consistent generation of magnetic fields in axion inflation models

TL;DR

This paper investigates how magnetic fields generated during axion inflation evolve through post-inflationary processes, including tachyonic instability, parametric resonance, and inverse cascade, to assess their potential to explain observed cosmic magnetic fields.

Contribution

It provides a comprehensive, self-consistent analysis of magnetic field generation and evolution in axion inflation models, incorporating post-inflationary effects often neglected.

Findings

Magnetic fields from inflation can reach ~10^{-19} G after evolution.

Modes near the end of inflation dominate the magnetic field contribution.

Post-inflationary processes significantly amplify the magnetic fields.

Abstract

There has been a growing evidence for the existence of magnetic fields in the extra-galactic regions, while the attempt to associate their origin with the inflationary epoch alone has been found extremely challenging. We therefore take into account the consistent post-inflationary evolution of the magnetic fields that are originated from vacuum fluctuations during inflation. In the model of our interest, the electromagnetic (EM) field is coupled to a pseudo-scalar inflaton $\phi$ through the characteristic term $\phi F\tilde F$, breaking the conformal invariance. This interaction dynamically breaks the parity and enables a continuous production of only one of the polarization states of the EM field through tachyonic instability. The produced magnetic fields are thus helical. We find that the dominant contribution to the observed magnetic fields in this model comes from the modes that leave the horizon near the end of inflation, further enhanced by the tachyonic instability right after the end of inflation. The EM field is subsequently amplified by parametric resonance during the period of inflaton oscillation. Once the thermal plasma is formed (reheating), the produced helical magnetic fields undergo a turbulent process called inverse cascade, which shifts their peak correlation scales from smaller to larger scales. We consistently take all these effects into account within the regime where the perturbation of $\phi$ is negligible and obtain $B_{\rm eff} \sim 10^{-19}$G, indicating the necessity of additional mechanisms to accommodate the observations.