Boltzmann or Bogoliubov? A Case of Gravitational Particle Production

Despite its weakness, gravity is the primordial source of particle production in the early Universe. All the particles, including dark matter, can inevitably be created after the end of inflation through gravity. To study this production channel, two different approaches have commonly been considered, one of which is based on the Boltzmann equation, and the other is based on the Bogoliubov transformation. The former approach has widely been used in phenomenological studies of dark matter, while the latter has been developed to describe particle production in curved spacetime. I will discuss when these two approaches are equivalent and when they are not by considering the pure gravitational production of a scalar particle.