Di Wu, Yifan Hu, Kohei Kamada

The generation of helical magnetic fields and the associated chiral asymmetry via the chiral anomaly is a generic feature in pseudoscalar inflation. In the presence of a Chern--Simons coupling between the inflaton and a U(1) gauge field, the homogeneous evolution of the inflaton induces a tachyonic instability in one circular polarization of the gauge field, resulting in the production of helical magnetic fields. In this work, we show that, in the case of a gauged lepton flavor symmetry, U(1)$_{L_i-L_j}$, this mechanism can lead to the generation of a sizable lepton asymmetry. In a simple setup, however, the resulting lepton asymmetry is typically too small to have an observational consequences, even setting aside constraints from baryon overproduction via sphaleron processes, due to the backreaction of the produced gauge fields and fermions on the inflationary dynamics. We demonstrate that this limitation can be overcome by implementing a mechanism to suppress fermion production during inflation. As a result, a much larger lepton asymmetry can be generated from the subsequent decay of magnetic helicity. Remarkably, for the gauged U(1)$_{L_μ-L_τ}$ symmetry, the generated asymmetry can be sufficiently large to suppress the primordial helium abundance, as may be inferred from recent cosmic microwave background observations by ACT.