We discuss in detail the primordial production of dark matter by a classical inflaton field after inflation. During preheating, the oscillation of the inflaton background with a large amplitude can lead to intense particle production for a short period of time. One may apply this idea to explain the current relic abundance of dark matter within the minimal extension of the Standard Model. Based on minimalism, we study different production mechanisms of dark matter with the simplest set of renormalizable interactions. We also find that Planck-suppressed operators can lead to efficient particle production and can alone account for all the dark matter in the Universe.
