Constraints on Primordial Magnetic Fields from Inflation

TL;DR

This paper derives model-independent bounds on primordial magnetic fields generated during inflation, showing that their strength is limited by reheating temperature and back-reaction effects, with implications for inflationary magnetogenesis theories.

Contribution

It provides the first generic, model-independent bounds on inflation-produced magnetic fields considering both quantum and classical growth mechanisms.

Findings

Magnetic fields of 10^{-15} G require reheating temperatures below ~100 MeV.

Quantum mechanical scenarios face even stronger constraints.

Back-reaction from electric fields limits magnetic field strength during inflation.

Abstract

We present generic bounds on magnetic fields produced from cosmic inflation. By investigating field bounds on the vector potential, we constrain both the quantum mechanical production of magnetic fields and their classical growth in a model independent way. For classical growth, we show that only if the reheating temperature is as low as T_{reh} <~ 10^2 MeV can magnetic fields of 10^{-15} G be produced on Mpc scales in the present universe. For purely quantum mechanical scenarios, even stronger constraints are derived. Our bounds on classical and quantum mechanical scenarios apply to generic theories of inflationary magnetogenesis with a two-derivative time kinetic term for the vector potential. In both cases, the magnetic field strength is limited by the gravitational back-reaction of the electric fields that are produced simultaneously. As an example of quantum mechanical scenarios, we construct vector field theories whose time diffeomorphisms are spontaneously broken, and explore magnetic field generation in theories with a variable speed of light. Transitions of quantum vector field fluctuations into classical fluctuations are also analyzed in the examples.