The exact WKB for cosmological particle production

TL;DR

This paper applies the Exact WKB method to analyze cosmological particle production, linking Stokes phenomena and scattering effects, and explores complex interactions and fermionic preheating.

Contribution

It introduces the use of the Exact WKB method for cosmological particle production, providing new insights into interactions and classical scattering effects.

Findings

EWKB simplifies calculations of particle production.

Classical scattering impacts particle creation processes.

Analysis of fermionic preheating via Landau-Zener model.

Abstract

The Bogoliubov transformation in cosmological particle production can be explained by the Stokes phenomena of the corresponding ordinary differential equation. The calculation becomes very simple as far as the solution is described by a special function. Otherwise, the calculation requires more tactics, where the Exact WKB (EWKB) may be a powerful tool. Using the EWKB, we discuss cosmological particle production focusing on the effect of more general interaction and classical scattering. The classical scattering appears when the corresponding scattering problem of the Schr\"odinger equation develops classical turning points on the trajectory. The higher process of fermionic preheating is also discussed using the Landau-Zener model.