ETHOS -- An Effective Theory of Structure Formation: Impact of Dark Acoustic Oscillations on Cosmic Dawn

Upcoming data of the 21-cm hydrogen line during cosmic dawn ($z\sim 10-30$) will revolutionize our understanding of the astrophysics of the first galaxies. Here we present a case study on how to exploit those same measurements to learn about the nature of dark matter (DM) at small scales. Focusing on the Effective Theory of Structure Formation (ETHOS) paradigm, we run a suite of simulations covering a broad range of DM microphysics, connecting the output of $N$-body simulations to dedicated 21-cm simulations to predict the evolution of the 21-cm signal across the entire cosmic dawn. We find that observatories targeting both the global signal and the 21-cm power spectrum are sensitive to all ETHOS models we study, and can distinguish them from CDM if the suppression wavenumber is smaller than $k\approx 300\, h/$Mpc, even when accounting for feedback with a phenomenological model. This is an order of magnitude smaller comoving scales than currently constrained by other data sets, including the Lyman-$\alpha$ forest. Moreover, if a prospective 21-cm detection confirmed a deficiency of power at small scales, we show that ETHOS models with strong dark acoustic oscillations can be discriminated from the pure suppression of warm dark matter, showing the power of 21-cm data to understand the behavior of DM at the smallest physical scales.