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We investigate pair creation by an electric field in four-dimensional deSitter space. The expectation value of the induced current is computed, usingthe method of adiabatic regularization. Under strong electric fields thebehavior of the current is similar to that in flat space, while under weakelectric fields the current becomes inversely proportional to the mass squaredof the charged field. Thus we find that the de Sitter space obtains a largeconductivity under weak electric fields in the presence of a charged field witha tiny mass. We then apply the results to constrain electromagnetic fields inthe early universe. In particular, we study cosmological scenarios forgenerating large-scale magnetic fields during the inflationary era. Electricfields generated along with the magnetic fields can induce sufficiently largeconductivity to terminate the phase of magnetogenesis. For inflationarymagnetogenesis models with a modified Maxwell kinetic term, the generatedmagnetic 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 theHubble scale or smaller exists in the Lagrangian. Similar constraints from theSchwinger effect apply for other magnetogenesis mechanisms.

Schwinger Effect in 4D de Sitter Space and Constraints on Magnetogenesis in the Early Universe