An analytic evaluation of gravitational particle production of fermions via Stokes phenomenon

TL;DR

This paper extends analytic methods based on the Stokes phenomenon to evaluate gravitational particle production of fermions, providing accurate, non-numerical solutions and insights into particle creation in curved spacetime.

Contribution

It develops an analytic framework for fermionic gravitational particle production using the EWKB method, generalizing previous bosonic results and deriving a universal connection matrix.

Findings

Analytic expression for the connection matrix valid to all orders.

Excellent agreement between analytic and numerical solutions.

Insights into catastrophic particle production for spin-3/2 fields.

Abstract

The phenomenon of gravitational particle production can take place for quantum fields in curved spacetime. The abundance and energy spectrum of gravitationally produced particles is typically calculated by solving the field's mode equations on a time-dependent background metric. For purposes of studying dark matter production in an inflationary cosmology, these mode equations are often solved numerically, which is computationally intensive, especially for the rapidly-oscillating high-momentum modes. However, these same modes are amenable to analytic evaluation via the Exact Wentzel-Kramers-Brillouin (EWKB) method, where gravitational particle production is a manifestation of the Stokes phenomenon. These analytic techniques have been used in the past to study gravitational particle production for spin-0 bosons. We extend the earlier work to study 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 perturbations) 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. We discuss the implications for an analytic understanding of catastrophic particle production due to vanishing sound speed, which can occur for a spin-3/2 Rarita-Schwinger field.