Chirality production during axion inflation

Abstract

We study the generation of the chiral charge during axion inflation where the pseudoscalar inflaton field $\varphi$ couples axially to the electromagnetic field through the term $(\beta /M_p)\varphi \mathbf{E}\cdot \mathbf{B}$ with dimensionless coupling constant $\beta$. To describe the evolution of electromagnetic field and determine $⟨\mathbf{E}\cdot \mathbf{B}⟩$ 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 ${\mathbf{j}}_{\mathrm{CME}}=e^2/(2{\pi }^2){\mu }_5\mathbf{B}$, 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.

arXiv comment13 pages, 2 figures. arXiv admin note: text overlap with arXiv:2109.01651

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• First-order CP phase transition in two-flavor QCD at $\theta =\pi$ under electromagnetic scale anomaly via a Nambu-Jona-Lasinio description
• Vector dark matter production during inflation in the gradient-expansion formalism