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

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 timedependent 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.

QFT approach to dressed particle processes in preheating and non-perturbative mechanism in kinematically-forbidden regime

“…2, the compact formula (2.31) may be a bit unsatisfactory as the background fields are Taylor expanded up to only the lowest order ∼ t and hence non-linear effects beyond the linear approximation, which can be important for non-adiabatic fields, cannot be described. For instance, our treatment cannot be applied when multiple particle production events equally contribute to particle production, for which, e.g., quantum interference between different production events occur and the production number is significantly modified [25,[40][41][42][43][44][45][46][47][48][49][50][51]. Such a multiple particle production would be relevant in the preheating, e.g., if the parent particle is light so that the exponential suppression in the parent particle-number density is not small enough.…”

“…A possible avenue to deal with more general background fields is semi-classical methods. Indeed, recent developments in understanding of the WKB method [25,42,[46][47][48][51][52][53][54][55][56] would enable us to address the non-perturbative dressed mode function in more general backgrounds. The semi-classical approach would also help us to develop more physical understandings of the kinematically-forbidden process (e.g., the production time).…”