Freezing-in a hot bath: resonances, medium effects and phase transitions

Relic density calculations of dark matter freezing out from the primordial plasma have reached a high level of sophistication, with several numerical tools readily available that match the observationally required accuracy. Dark matter production via the freeze-in mechanism, on the other hand, is sensitive to much higher temperatures than in the freeze-out case, implying both technical and computational difficulties when aiming for the same level of precision. We revisit the formulation of freeze-in production in a way that facilitates the inclusion of in-medium corrections like plasma effects and the spin statistics of relativistic quantum gases, as well as the temperature dependence of dark matter production rates induced by the electroweak and strong phase transitions, and we discuss in detail the additional complications arising in the presence of $s$-channel resonances. We illustrate our approach in the context of Higgs portal models, and provide the most accurate calculation to date of the freeze-in abundance of Scalar Singlet dark matter. We explore in particular the case of small reheating temperatures, for which the couplings implied by the freeze-in mechanism may be testable at the LHC. Together with this article we present a major update 6.3 of DarkSUSY with the added capability of performing general freeze-in calculations, including all complications mentioned above.