  In this work we consider the most general electromagnetic theory in curved
space-time leading to linear second order differential equations, including
non-minimal couplings to the space-time curvature. We assume the presence of a
temporal electromagnetic background whose energy density plays the role of dark
energy, as has been recently suggested. Imposing the consistency of the theory
in the weak-field limit, we show that it reduces to standard electromagnetism
in the presence of an effective electromagnetic current which is generated by
the momentum density of the matter/energy distribution, even for neutral
sources. This implies that in the presence of dark energy, the motion of
large-scale structures generates magnetic fields. Estimates of the present
amplitude of the generated seed fields for typical spiral galaxies could reach
$10^{-9}$ G without any amplification. In the case of compact rotating objects,
the theory predicts their magnetic moments to be related to their angular
momenta in the way suggested by the so called Schuster-Blackett conjecture.
