Chirality Production during Axion Inflation

Abstract

We study the generation of a chiral charge during the axion inflation, where the pseudoscalar inflaton field φ couples axially to the electromagnetic field via the term (β/Mp)φ E · B with the dimensionless coupling constant β. To describe the evolution of the electromagnetic field and to determine ⟨E·B⟩ sourcing the chiral asymmetry during the inflation due to the chiral anomaly, we employ the gradient-expansion formalism. It operates with a set of vacuum expectation values of the bilinear electromagnetic functions and allows us to consider the backreaction of generated fields on the inflaton evolution, as well as the Schwinger production of charged fermions. In addition, we assume that the produced fermions thermalize and include the chiral magnetic effect contribution to the electric current given by jCME = e2/(2π2)μ5B, where μ5 is the chiral chemical potential which quantifies the produced chiral asymmetry. Solving a set of equations for the inflaton field, scale factor, quadratic functions of the electromagnetic field, and the chiral charge density (chiral chemical potential), we find that the chirality production is quite efficient leading to the generation of a large chiral chemical potential at the end of the axion inflation.