We study the amplification of large-scale magnetic fields during preheating
and inflation in several different models. Preheating can resonantly ampli
fy seed fields on cosmological scales. In the presence of conductivity, how
ever, the effect of resonance is typically weakened and the amplitude of pr
oduced magnetic fields depends sensitively on the evolution of conductivity
during the preheating and thermalization phases. In addition we discuss ge
ometric magnetization, where amplification of magnetic fields occurs throug
h coupling to curvature invariants. This can be efficient during inflation
due to a negative coupling instability. Finally we discuss the breaking of
the conformal flatness of the background metric whereby magnetic fields can
be stimulated through the growth of scalar metric perturbations during met
ric preheating.