Title: Separating Dark Acoustic Oscillations from Astrophysics at Cosmic Dawn

Abstract: The formation redshift and abundance of the first stars and galaxies is highly sensitive to the build up of low mass dark matter halos as well as astrophysical feedback effects which modulate star formation in these low mass halos. The 21-cm signal at cosmic dawn will depend strongly on the formation of these first luminous sources and thus can be used to constrain unknown astrophysical and dark matter properties in the early universe. In this paper, we explore how well we could measure properties of dark matter using the 21-cm power spectrum at $z>10$, given unconstrained astrophysical parameters. We create a generalizable form of the dark matter halo mass function for models with damped and/or oscillatory linear power spectra, finding a single "smooth-k" window function which describes a broad range of models including CDM. We use this to make forecasts for structure formation using the Effective Theory of Structure Formation (ETHOS) framework to explore a broad parameter space of dark matter models. We make predictions for the 21-cm power spectrum observed by HERA varying both cosmological ETHOS parameters as well as astrophysical parameters. Using a Markov Chain Monte Carlo forecast we find that the ETHOS dark matter parameters are degenerate with astrophysical parameters linked to star formation in low mass dark matter halos but not with X-ray heating produced by the first generation of stars. After marginalizing over uncertainties in astrophysical parameters we demonstrate that with just 540 days of HERA observations it should be possible to distinguish between CDM and a broad range of dark matter models with suppression at wavenumbers $k\lesssim 200\,h$Mpc$^{-1}$ assuming a moderate noise level. These results demonstrate the potential of 21-cm observations to constrain the matter power spectrum on scales smaller than current probes.