Direct millicharged dark matter cannot explain the EDGES signal

Heat transfer between baryons and millicharged dark matter has been invoked as a possible explanation for the anomalous 21-cm absorption signal seen by EDGES. Prior work has shown that the solution requires that millicharged particles make up only a fraction $(m_\chi/{\rm MeV})\ 0.0115\% \lesssim f \lesssim 0.4\%$ of the dark matter and that their mass $m_\chi$ and charge $q_\chi$ have values $0.1 \lesssim (m_\chi/{\rm MeV})\lesssim 10$ and $10^{-6} \lesssim (q_\chi/e)\lesssim 10^{-4}$. Here we show that such particles come into chemical equilibrium before recombination, and so are subject to a constraint on the effective number $N_{\rm eff}$ of relativistic degrees of freedom, which we update using Planck 2018 data. We moreover determine the precise relic abundance $f$ that results for a given mass $m_\chi$ and charge $q_\chi$ and incorporate this abundance into the constraints on the millicharged-dark-matter solution to EDGES. With these two results, the solution is ruled out if the relic abundance is set by freeze-out.