Origin of cosmic magnetic fields: Superadiabatically amplified modes in open Friedmann universes

Abstract

Cosmological magnetic fields in open Friedmann universes can experience superadiabatic amplification within the realm of conventional electromagnetism. This is possible mathematically, despite the conformal invariance of Maxwell's equations, because Friedmann spacetimes with non-Euclidean spatial geometry are not globally conformal to Minkowski space. Physically, this means that even universes that are marginally open today can sustain large-scale magnetic fields that are substantially stronger than previously anticipated. In the present article, we investigate this purely geometric amplification mechanism in greater detail, focusing on the early evolution of the electromagnetic modes in inflationary Friedmann models with hyperbolic spatial geometry. This also allows us to refine the earlier numerical estimates and provide the current spectrum of the residual, superadiabatically amplified magnetic field.