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 $\sigma(A_{\rm
CIP})= 10^{-3}-10^{-4}$, comparable to the sensitivity of upcoming CMB
experiments, and potentially exceeding the constraints from cosmic-variance
limited BAO surveys.
