To $B$ or not to $B$: Primordial magnetic fields from Weyl anomaly

TL;DR

This paper critically examines the hypothesis that Weyl anomaly in quantum electrodynamics can generate primordial magnetic fields in the early universe, concluding that it cannot produce classical magnetic fluctuations from vacuum states.

Contribution

The study provides a detailed analysis beyond the weak gravitational limit, demonstrating that Weyl anomaly does not convert quantum gauge fluctuations into classical magnetic fields.

Findings

Weyl anomaly does not produce classical magnetic fields from vacuum fluctuations.

The effective action analysis shows no magnetic field generation in the early universe.

The results hold regardless of the number of massless charged particles.

Abstract

The quantum effective action for the electromagnetic field in an expanding universe has an anomalous dependence on the scale factor of the metric arising from virtual charged particles in the loops. It has been argued that this Weyl anomaly of quantum electrodynamics sources cosmological magnetic fields in the early universe. We examine this long-standing claim by using the effective action beyond the weak gravitational field limit which has recently been determined. We introduce a general criteria for assessing the quantumness of field fluctuations, and show that the Weyl anomaly is not able to convert vacuum fluctuations of the gauge field into classical fluctuations. We conclude that there is no production of coherent magnetic fields in the universe from the Weyl anomaly of quantum electrodynamics, irrespective of the number of massless charged particles in the theory.