  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.
