Hydrodynamical approach to chirality production during axion inflation

We study chirality production in the pseudoscalar inflation model of magnetogenesis taking into account the Schwinger effect and particle collisions in plasma in the relaxation time approximation. We consider the Schwinger production of one Dirac fermion species by an Abelian gauge field in two cases: (i) the fermion carries only the weak charge with respect to the U(1) group and (ii) it is also charged with respect to another strongly coupled gauge group. While the gradient-expansion formalism is employed for the description of the evolution of gauge field, plasma is described by hydrodynamical approach which allows us to determine the number, energy density, and chirality of produced fermions. It is found that while chirality production is very efficient for both, weakly and strongly interacting fermions, the resulting gauge field is typically stronger in the case of strongly interacting fermions due to suppression of the Schwinger conductivity by particle collisions.