Schwinger Effect in 4D de Sitter Space and Constraints on Magnetogenesis
  in the Early Universe
  We investigate pair creation by an electric field in four-dimensional de
Sitter space. The expectation value of the induced current is computed, using
the method of adiabatic regularization. Under strong electric fields the
behavior of the current is similar to that in flat space, while under weak
electric fields the current becomes inversely proportional to the mass squared
of the charged field. Thus we find that the de Sitter space obtains a large
conductivity under weak electric fields in the presence of a charged field with
a tiny mass. We then apply the results to constrain electromagnetic fields in
the early universe. In particular, we study cosmological scenarios for
generating large-scale magnetic fields during the inflationary era. Electric
fields generated along with the magnetic fields can induce sufficiently large
conductivity to terminate the phase of magnetogenesis. For inflationary
magnetogenesis models with a modified Maxwell kinetic term, the generated
magnetic fields cannot exceed 10^{-30} G on Mpc scales in the present epoch,
when a charged field carrying an elementary charge with mass of order the
Hubble scale or smaller exists in the Lagrangian. Similar constraints from the
Schwinger effect apply for other magnetogenesis mechanisms.
