Probing compensated isocurvature with the 21-cm signal during cosmic dawn

Upcoming measurements of the 21-cm line of neutral hydrogen will open a new observational window into the early stages of structure growth, providing a unique opportunity for probing large-scale cosmological signatures using the small-scale signals from the first stars. In this paper, we evaluate the detection significance of compensated isocurvature perturbations (CIPs) from observations of the 21-cm hydrogen line during the cosmic dawn era. CIPs are modulations of the relative baryon and dark-matter density that leave the total matter density unchanged. We find that, under different assumptions for feedback and foregrounds, the ongoing HERA and upcoming SKA1-low experiments will provide constraints on uncorrelated CIPs at the level of $\ensuremath{\sigma}({A}_{\mathrm{CIP}})={10}^{\ensuremath{-}3}\ensuremath{-}{10}^{\ensuremath{-}4}$, comparable to the sensitivity of upcoming cosmic microwave background experiments, and potentially exceeding the constraints from cosmic-variance limited baryon acoustic oscillation surveys.