  Cosmological particle production caused by a time-dependent scalar field is
commonly used in cosmology. In this paper, we analyze the possibility of direct
asymmetry production by cosmological particle production. Our focus is the
mechanism of asymmetry production when an 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 analyze
the mechanism of generating asymmetry in the decay of the
pseudo-Nambu-Goldstone boson. We also 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.
