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

Abstract

Cosmological particle production by a time-dependent scalar field is common in cosmology. We focus on the mechanism of asymmetry production when interaction explicitly violates symmetry and its motion is rapid enough to create particles by itself. Combining the exact WKB analysis and the Landau-Zener transition, we point out that perturbation before the non-perturbative analysis may drastically change the structure of the Stokes lines of the theory. The Exact WKB can play an important role in avoiding such discrepancies.

Superadiabatic basis in cosmological particle production: application to preheating

“…Bosonic particles are straightforward, and the same method is available. For fermions, one is able to apply the superadiabatic basis for two level quantum mechanical system [53,54], which is recently applied to the fermionic particle production in [14,55,56]. Since standard model mostly consists of fermions, such an analysis would be necessary for realistic cosmological models.…”

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

“…It is based on the pioneering work of Voros (1983) [68], and it has been developed by several groups [69,70]. In recent year this method has been employed [29,30,63,89] to study solutions of the oscillator equation χ (η) + ω 2 (η)χ(η) = 0 that appears in bosonic field theories. For a clear and concise review of the EWKB method, see e.g.…”

“…[63] and Appendix A of Ref. [30]. In this paper, we adapt the EWKB method to study the mode equations for spinor fields.…”

“…It can be understood as the gravitational analog of the Schwinger effect [9,10]. Although the phenomenon of GPP has not been observed directly, it is expected to play an important role in black hole evaporation via Hawking radiation [11], reheating after inflation [12][13][14], inflationary quantum fluctuations leading to the generation of primordial curvature perturbations [15][16][17][18], and the creation of cosmological relics such as dark matter [14,[19][20][21][22][23][24][25][26][27][28], baryon asymmetry [29,30] and primordial gravitational waves [31][32][33].…”

“…The EWKB method has been used to study GPP in bosonic field theories [63] where the field equation takes the form of a second-order oscillator equation, but it has seen limited application for fermionic theories [29,30] where the mode equation takes the form of a two-level Schrödinger equation. Our central goal is to provide a new derivation of the connection matrix for general theories of free fermions with spin-1/2 or 3/2.…”