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 $B_{rm eff} gtrsim 10^{-16}, {rm G}$, exhibiting a field strength $B_{rm phys} approx 10^{-13}, {rm G}$ and a correlation length $lambda_{rm phys}approx10, {rm pc}$. 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 $B_{rm eff}$. 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.
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