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.
Highlights
Of thermal equilibrium” condition in the famous Sakharov’s three conditions [4] since the time-dependent background violates CPT
The result can be regarded as asymmetric decay of the θ(t) field (PNGB), where the asymmetry is determined by the sign of θ
For ∆(t) = Ae2iω0t, the two states are shifted together to make a pair of degenerated states (D = 0) in H. If this transition corresponds to the Bogoliubov transformation, particle production is possible in this case
Summary
We review the original Landau-Zener model and explain how it can be related to cosmological particle production. Since these adiabatic states are diagonalizing the Hamiltonian and identified with the asymptotic WKB solutions, the transition matrix for these (adiabatic) states is giving Bogoliubov transformation of the cosmological particle production. Comparing the original equation of the Landau-Zener model and the decoupled equations, one can see that D1 ≡ −vt, D2 ≡ +vt in the (original) diagonal elements are transferred into the “potential” − 14 v2t2 in the decoupled equations [32]. In this paper, both approaches (the Landau-Zener model and the EWKB Stokes lines of the decoupled equations) are used to understand the cosmological particle production and the origin of the asymmetry
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