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

TL;DR

This paper explores particle production in strong electromagnetic fields, clarifies the chiral anomaly and Schwinger effect, and applies these concepts to axion inflation, highlighting the impact of fermion mass on cosmological signals.

Contribution

It provides a unified framework for understanding particle production, anomaly effects, and non-linearities in QED, and applies these insights to axion inflation models.

Findings

The chiral anomaly equation is explicitly derived in this context.

The induced current's dependence on fermion mass is characterized.

Scalar and gravitational wave spectra are highly sensitive to fermion mass.

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.