The exact WKB for cosmological particle production

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 Schrödinger equation develops classical turning points on the trajectory. The higher process of fermionic preheating is also discussed using the Landau-Zener model.

The exact WKB and the Landau-Zener transition for asymmetry in cosmological particle production

“…Due to the formal structure of the EWKB [32,35,36], the Stokes lines are drawn using only Q 0 . 4 Therefore, in the EWKB formulation, ψ 1 and ψ 2 have the same Stokes lines.…”

“…See also appendix B and ref. [32] for more details about the EWKB and the Stokes lines for cosmological particle production.…”

“…For the EWKB, this factor appears from the integral connecting the two turning points of the MTP [32]. (Here, "turning point" denotes solutions of Q 0 = 0.)…”

“…For Dirac fermions, one can find the calculation based on the Landau-Zener model in ref. [32], which can be compared with the standard calculation of refs. [40,41].…”

Chemical-potential-assisted particle production in FRW spacetimes

“…We note that there are many past studies in the literature that utilize the Stokes phenomenon to study particle production. For example, it is applied to the Sauter-Schwinger effect [38][39][40][41][42][43], to Hawking radiation [44], to the adiabatic particle number in global de Sitter (dS) spacetime [45][46][47], to dark matter production at the end of inflation [48], to preheating [49,50], and to particle production triggered by vacuum decay [51]. An excellent review is recently given in [52].…”