Heating of Baryons due to Scattering with Dark Matter During the Dark
  Ages
  We explore the effects of elastic scattering between dark matter and baryons
on the 21-cm signal during the dark ages. In particular, we consider a
dark-matter---baryon interaction with a cross section of the form $\sigma =
\sigma_0 v^{-4}$, in which case the effect of the drag force between the dark
matter and baryon fluids grows with time. We show that, as opposed to what was
previously thought, this effect heats up the baryons due to the relative
velocity between dark matter and baryons. This creates an additional source of
fluctuations, which can potentially make interactions easier to detect by 21-cm
measurements than by using the cosmic microwave background and the
Lyman-$\alpha$ forest. Our forecasts show that the magnitude of the cross
section can be probed to $\sigma_0\sim 3\times 10^{-42}$ cm$^2$ for
$m_{\chi}\ll 1$ GeV and $\sigma_0\sim 2 \times 10^{-41}\ (m_{\chi}/10\, \rm
GeV)$ cm$^2$ for $m_{\chi}\gg 1$ GeV with next generation experiments, and
improved to $\sigma_0\sim 4\times 10^{-44}$ cm$^2$ for $m_{\chi} \ll 1$ GeV and
$\sigma_0\sim 4 \times 10^{-43}\ (m_{\chi}/10\, \rm GeV)$ cm$^2$ for
$m_{\chi}\gg 1$ GeV with futuristic experiments.
