Analytically evaluating gravitational particle production of fermions via Stokes phenomenon

The phenomenon of gravitational particle production can take place for quantum fields in curved spacetime. The abundance of gravitationally produced particles is typically calculated by solving the field's mode equations on a time-dependent background metric. Alternatively, one can calculate the abundance analytically via the Exact Wentzel-Kramers-Brillouin (EWKB) method, where gravitational particle production is a manifestation of the Stokes phenomenon. We extend earlier works on applying this analytic method to study the gravitational production of spin-1/2 and spin-3/2 fermions. We derive an analytic expression for the connection matrix (valid to all orders in an adiabatic parameter) that relates Bogoliubov coefficients across a Stokes line connecting a merged pair of simple turning points. By comparing the analytic approximation with a direct numerical integration of the mode equations, we demonstrate an excellent agreement and highlight the utility of the Stokes phenomenon formalism applied to fermions.