Maximizing Direct Detection with Highly Interactive Particle Relic Dark Matter

We estimate the maximum direct detection cross section for sub-GeV dark matter (DM) scattering off nucleons. For DM masses in the range 10 keV-100 MeV, cross sections greater than 10^{-36}-10^{-30}  cm^{2} seem implausible. We present a DM candidate which realizes this maximum cross section: highly interactive particle relics (HYPERs). After HYPERs freeze-in, a dark sector phase transition decreases the mediator's mass. This increases the HYPER's direct detection cross section without impacting its abundance or measurements of big bang nucleosynthesis and the cosmic microwave background.