To $B$ or not to $B$: Primordial magnetic fields from Weyl anomaly
Résumé
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.
Mots clés
Anomalies in Field and String Theories
Effective Field Theories
Models of Quantum Gravity
anomaly: Weyl
gauge field theory: fluctuation
magnetic field: primordial
fluctuation: vacuum
charged particle: massless
space-time: expansion
quantum electrodynamics
effective action
electromagnetic field
gravitation
coherence