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Freeze-in dark matter (DM) mediated by a light ($\ll$ keV) weakly-coupleddark-photon is an important benchmark for the emerging low-mass directdetection program. Since this is one of the only predictive, detectablefreeze-in models, we investigate how robustly such testability extends to otherscenarios. For concreteness, we perform a detailed study of models in which DMcouples to a light scalar mediator and acquires a freeze-in abundance throughHiggs-mediator mixing. Unlike dark-photons, whose thermal properties weakenstellar cooling bounds, the scalar coupling to Standard Model (SM) particles issubject to strong astrophysical constraints, which severely limit the fractionof DM that can be produced via freeze-in. While it seems naively possible tocompensate for this reduction by increasing the mediator-DM coupling,sufficiently large values eventually thermalize the dark sector with itself andyield efficient DM annihilation to mediators, which depletes the freeze-inpopulation; only a small window of DM candidate masses near the $\sim$ GeVscale can accommodate the total observed abundance. Since many qualitativelysimilar issues arise for other light mediators, we find it genericallydifficult to realize a viable freeze-in scenario in which production arisesonly from renormalizable interactions with SM particles. We also comment onseveral model variations that may evade these conclusions.

Freezing In, Heating Up, and Freezing Out: Predictive Nonthermal Dark Matter and Low-Mass Direct Detection