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 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.

33 pages + appendices and references, 10 figures

References in corpus (17)

• The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses
• Gravitational Production of Dark Matter during Reheating
• Gravitational Effects on Inflaton Decay
• Gravitational portals in the early Universe
• Super-Adiabatic Particle Number in Schwinger and de Sitter Particle Production
• Gravitational Portals with Non-Minimal Couplings
• Exact WKB analysis of the vacuum pair production by time-dependent electric fields
• Higgs condensation as an unwanted curvaton
• Chemical-Potential-Assisted Particle Production in FRW Spacetimes
• Catastrophic Production of Slow Gravitinos
• Gravitino Problem in Minimal Supergravity Inflation
• Gravitational production of nearly thermal fermionic Dark Matter
• Stokes phenomenon and gravitational particle production -- How to evaluate it in practice
• Slow and Safe Gravitinos
• The Exact WKB and the Landau-Zener transition for asymmetry in cosmological particle production
• Superadiabatic basis in cosmological particle production: application to preheating
• Stokes phenomenon and Hawking Radiation

Cited by in corpus (7)

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• Gravitationally produced Dark Matter and primordial black holes
• Logarithmic catastrophes and Stokes's phenomenon in waves at horizons
• QFT approach to dressed particle processes in preheating and non-perturbative mechanism in kinematically-forbidden regime
• Roles of electric field/time-dependent Wilson line in toroidal compactification with or without magnetic fluxes
• More on scattering processes of dressed particles with a time-dependent mass