Effect of a magnetic field on Schwinger mechanism in de Sitter spacetime

We investigate the effect of a uniform magnetic field background on scalar QED pair production in a four-dimensional de Sitter spacetime (${\mathrm{dS}}_4$). We obtain a pair production rate which agrees with the known Schwinger result in the limit of Minkowski spacetime and with Hawking radiation in dS spacetime 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 calculate the induced current and examine 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 $E·B$, while in the infrared regime, it responds as $B/E$, which leads to a phenomenon of infrared hyperconductivity. These results for the induced current have important applications for the cosmic magnetic field evolution.

Figure 1

The normalized induced current $J/e{H}^3$ (upper surface) and semiclassical current $J_{\mathrm{sem}}/e{H}^3$ (lower surface) are plotted as functions of $\lambda$ and $\ell$, in the lowest Landau state $n=0$ with $\mu =1$.

Figure 2

For different values of $\ell$, the normalized induced current $J/e{H}^3$ is plotted as a function of $\lambda$, in the lowest Landau state $n=0$ with $\mu =1$.

Figure 3

For different values of $\lambda$, the normalized induced current $J/e{H}^3$ is plotted as a function of $\ell$, in the lowest Landau state $n=0$ with $\mu =1$.