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We study the atomic physics and the astrophysical implications of a model inwhich the dark matter is the analog of hydrogen in a secluded sector. The selfinteractions between dark matter particles include both elastic scatterings aswell as inelastic processes due to a hyperfine transition. The self-interactioncross sections are computed by numerically solving the coupled Schr\"{o}dingerequations for this system. We show that these self interactions exhibit theright velocity dependence to explain the low dark matter density cores seen insmall galaxies while being consistent with all constraints from observations ofclusters of galaxies. For a viable solution, the dark hydrogen mass has to bein 10--100 GeV range and the dark fine-structure constant has to be larger than0.02. Precisely for this range of parameters, we show that significant coolinglosses may occur due to inelastic excitations to the hyperfine state andsubsequent decays, with implications for the evolution of low-mass halos andthe early growth of supermassive black holes. Cooling from excitations tohigher $n$ levels of dark hydrogen and subsequent decays is possible at thecluster scale, with a strong dependence on halo mass. Finally, we show that theminimum halo mass is in the range of $10^{3.5}$ to $10^7 M_\odot$ for theviable regions of parameter space, significantly larger than the typicalpredictions for weakly-interacting dark matter models. This pattern ofobservables in cosmological structure formation is unique to this model, makingit possible to rule in or rule out hidden sector hydrogen as a viable darkmatter model.

Hidden Sector Hydrogen as Dark Matter: Small-scale Structure Formation Predictions and the Importance of Hyperfine Interactions