Fermionic current and Schwinger effect in de Sitter spacetime

We study the fermionic Schwinger effect in two-dimensional de Sitter spacetime. To do so, we first present a method to semiclassically compute the number of pairs created per momentum mode for general time dependent fields. In addition, the constant electric field is studied in depth. In this case, solutions for the Dirac equation can be found and the number of pairs can be computed using the standard Bogoliubov method. This result is shown to agree with the semiclassical one in the appropriate limit. The solutions are also used to compute the expectation value of the induced current. Comparing these results to similar studies for bosons, we find that while the results agree in the semiclassical limit, they do not generally agree. In particular, there is no occurrence of a strong current for small electric fields.