We present a thorough analysis of the sequential freeze-in mechanism for dark matter production in the early universe. In this mechanism the dark matter relic density results from pair annihilation of mediator particles which are themselves produced by thermal collisions of standard model particles. Below some critical value of the mediator coupling to standard model fields, this sequential channel dominates over the usual freeze-in where dark matter is directly produced from thermal collisions, even when the mediator is not in thermal equilibrium. The latter case requires computing the full non-thermal distribution of the mediators, for which finite temperature corrections are particularly important.
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