In this work we compute the production of magnetic fields in models of axion inflation coupled to the hypercharge sector of the Standard Model through a Chern-Simons interaction term .
We make the simplest choice of a quadratic inflationary potential and use lattice simulations to calculate the magnetic field strength , helicity and correlation length at the end of inflation .
For small values of the axion-gauge field coupling strength the results agree with no-backreaction calculations and estimates found in the literature .
For larger couplings the helicity of the magnetic field differs from the no-backreaction estimate and depends strongly on the comoving wavenumber .
We estimate the post-inflationary evolution of the magnetic field based on known results for the evolution of helical and non-helical magnetic fields .
The magnetic fields produced by axion inflation with large couplings to U ( 1 ) _ { Y } can reach B _ { eff } \gtrsim 10 ^ { -16 } { G } , exhibiting a field strength B _ { phys } \approx 10 ^ { -13 } { G } and a correlation length \lambda _ { phys } \approx 10 { pc } .
This result is insensitive to the exact value of the coupling , as long as the coupling is large enough to allow for instantaneous preheating .
Depending on the assumptions for the physical processes that determine blazar properties , these fields can be found consistent with blazar observations based on the value of B _ { eff } .
Finally , the intensity of the magnetic field for large coupling can be enough to satisfy the requirements for a recently proposed baryogenesis mechanism , which utilizes the chiral anomaly of the Standard Model .