Inflationary magnetogenesis and non-local actions: The conformal anomaly

TL;DR

This paper explores how the conformal anomaly in quantum electrodynamics during inflation can generate magnetic fields with a blue spectrum, potentially explaining intergalactic magnetic fields.

Contribution

It demonstrates that the non-local effective action from QED's conformal anomaly can produce magnetic fields during inflation with specific spectral properties.

Findings

Magnetic field spectrum is blue with index n_B ≈ 2 - α_e.

The sign of the beta function influences the magnetic field generation.

A low reheating temperature is necessary for current magnetic field bounds.

Abstract

We discuss the possibility of successful magnetogenesis during inflation by employing the one-loop effective action of massless QED. The action is strictly non-local and results from the long distance fluctuations of massless charged particles present at the inflationary scale. Most importantly, it encodes the conformal anomaly of QED which is crucial to avoid the vacuum preservation in classical electromagnetism. In particular, we find a blue spectrum for the magnetic field with spectral index $n_B \simeq 2 - \alpha_{\text{e}}$ where $\alpha_{\text{e}}$ depends on both the number of e-folds during inflation as well as the coefficient of the one-loop beta function. In particular, the sign of the beta function has important bearing on the final result. A low reheating temperature is required for the present day magnetic field to be consistent with the lower bound inferred on the field in the intergalactic medium.