Consistent generation of magnetic fields in axion inflation models

Abstract

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