Chiral Anomaly, Schwinger Effect, Euler-Heisenberg Lagrangian, and application to axion inflation

Abstract

Particle production in strong electromagnetic fields is a recurring theme in solid state physics, heavy ion collisions, early universe cosmology and formal quantum field theory. In this paper we discuss the Dirac equation in a background of parallel electric and magnetic fields. We review the Schwinger particle production rate, clarify the emergence of the chiral anomaly equation and compute the induced current of charged fermions. We distinguish the contributions from non-perturbative particle production, from the running of the gauge coupling constant and from non-linearities in the effective QED Lagrangian, and clarify how these contributions arise within a single framework. We apply these results to axion inflation. A Chern-Simons coupling between the pseudoscalar particle driving cosmic inflaton and an abelian gauge group induces a dual production of gauge fields and charged fermions. We show that the resulting scalar and gravitational wave power spectra strongly depend on the fermion mass.

45 pages, 9 figures; v2: typos fixed, published version

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Cited by in corpus (7)

• Scalar field couplings to quadratic curvature and decay into gravitons
• Universality of linear perturbations in SU($N$)-natural inflation
• Gravitational waves from axion inflation in the gradient expansion formalism. Part I. Pure axion inflation
• Fate of the first-order chiral phase transition in QCD: Implications for dark QCD studied via a Nambu-Jona-Lasinio model
• Gravitational waves from axion inflation in the gradient expansion formalism. Part II. Fermionic axion inflation
• Induced energy-momentum tensor in de Sitter scalar QED and its implication for induced current
• First-order CP phase transition in two-flavor QCD at $\theta =\pi$ under electromagnetic scale anomaly via a Nambu-Jona-Lasinio description