Chirality production during axion inflation

TL;DR

This paper investigates how chiral charge is generated during axion inflation through electromagnetic field interactions, employing a formalism that accounts for backreaction and fermion production, revealing efficient chirality production.

Contribution

It introduces a gradient expansion formalism to model electromagnetic and chiral charge evolution during axion inflation, including backreaction and the chiral magnetic effect.

Findings

Chirality production is highly efficient during axion inflation.

Large chiral chemical potentials can be generated by the end of inflation.

The formalism accounts for backreaction and fermion production effects.

Abstract

We study the generation of the chiral charge during axion inflation where the pseudoscalar inflaton field $\phi$ couples axially to the electromagnetic field through the term $(\beta/M_p)\phi\,\boldsymbol{E}\cdot\boldsymbol{B}$ with dimensionless coupling constant $\beta$. To describe the evolution of electromagnetic field and determine $\langle\boldsymbol{E}\cdot\boldsymbol{B}\rangle$ sourcing the chiral asymmetry during inflation due to the chiral anomaly, we employ the gradient expansion formalism. It operates with a set of vacuum expectation values of bilinear electromagnetic functions and allows us to take into account the backreaction of generated fields on the inflaton evolution as well as the Schwinger production of charged fermions. In addition, we include the chiral magnetic effect contribution to the electric current $\boldsymbol{j}_{\rm CME}=e^{2}/(2\pi^2)\mu_{5}\boldsymbol{B}$, where $\mu_5$ is the chiral chemical potential which quantifies the chiral charge production. 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 chemical potential at the end of axion inflation.