We investigate the effect of a constant magnetic field background on the scalar QED pair production in a four-dimensional de Sitter spacetime ($dsf$). We have obtained the pair production rate which agrees with the known Schwinger result in the limit of Minkowski spacetime and with the Hawking radiation in de Sitter spacetime (dS) in the zero electric field limit. Our results describe how the cosmic magnetic field affects the pair production rate in cosmological setups. In addition, using the zeta function regularization scheme we have calculated the induced current and examined the effect of a magnetic field on the vacuum expectation value of the current operator. We find that, in the case of a strong electromagnetic background the current responds as $Ecdot B$, while in the infrared regime, it responds as $B/E$, which leads to a phenomenon of infrared hyperconductivity. These results of the induced current have important applications for the cosmic magnetic field evolution.
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