Cosmological particle production as Stokes phenomena

Particle production from “vacuum” takes place in time-dependent backgrounds. In very early universe, particularly just after inflation, expanding metric as well as oscillating scalar fields play the role of such backgrounds. Mathematically, “particle production from vacuum” can be understood as “Stokes phenomena”, and such understanding enables us to estimate the amount of produced particles in a systematic way. In this talk, I will review the relation between Stokes phenomena and particle production. Then, from the Stokes phenomena viewpoint, I will (re)consider particle production associated with expanding universe, an oscillating scalar field, or both of them. I will also discuss the time evolution of particle number, and its relation to the ambiguity of “vacuum states”.