Gravitational particle production as Stokes phenomenon

In nontrivial time-dependent backgrounds, particles can be produced from a “vacuum” . Such particle production may play important roles e.g. in the early Universe. Mathematically, we can understand such particle production from the asymptotic behavior of mode functions defining “particles”. In particular, the so called “Stokes phenomenon” is crucial for the asymptotic behavior. In this talk, first I will review some basics of quantum field theory in time-dependent backgrounds for free fields and discuss the relation between the Stokes phenomenon and “particle production from a vacuum”. Then, I will show specific examples of gravitational particle production, from which we can learn how to evaluate the particle production rates in practice.