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.