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 $(m_{\chi }/\mathrm{MeV})0.0115\%\lesssim f\lesssim 0.4\%$ of the dark matter and that their mass $m_{\chi }$ and charge $q_{\chi }$ have values $0.1\lesssim (m_{\chi }/\mathrm{MeV})\lesssim 10$ 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 $N_{\mathrm{eff}}$ 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 the EDGES signal. With these two results, the solution is ruled out if the relic abundance is set by freeze-out.

Figure 1

The sum of thermal cross sections between all charged Dirac fermions in the Standard Model and a millicharged particle with a mass $m_{\chi }\in \{1\mathrm{MeV},10\mathrm{MeV},100\mathrm{MeV}\}$ and a charge $q_{\chi }={10}^{-6}e$. For temperatures higher than the electron mass this expression follows the expected Coulombic scaling relation $x^2\sim T^{-2}$, while exponentially cutting off at lower temperatures. There is a period, however, below the millicharge mass, where the thermal cross section is constant, though only when the millicharge mass is larger than the electron mass. The discrete jump is due to the change in particle content at the QCD crossover.

Figure 2

The abundance of a $m_{\chi }=1\mathrm{MeV}$ millicharged particle with a charge $q_{\chi }\in \{{10}^{-6}e,{10}^{-8.3},{10}^{-10.1}e\}$, evolved with Eq. (3). For the $q_{\chi }={10}^{-6}e$ case, the particle thermalizes at around 100 GeV. Otherwise, it never reaches chemical equilibrium, represented by $Y_{\chi }^{\mathrm{eq}}$. For the $q_{\chi }={10}^{-10.1}e$ scenario the abundance is set by freeze- in and can achieve the same relic abundance as freeze- out with $q_{\chi }={10}^{-6}e$. However such charges are too small to produce the EDGES signal.

Figure 3

The numerically calculated freeze-out abundances ${\mathrm{\Omega }}_{\chi }$ of a Dirac fermion with mass $m_{\chi }=1\mathrm{MeV}$ and charge $q_{\chi }\in \{{10}^{-6}e,{10}^{-5}e,{10}^{-4}e\}$. Its equilibrium abundance $Y_{\chi }^{\mathrm{eq}}$ is plotted for reference.

Figure 4

The DM fraction $f$ of millicharged particles with a mass $m_{\chi }$ and a charge $q_{\chi }$ for Dirac fermions (DF). At a fixed mass, the abundance decreases with increasing charge. At a fixed charge the abundance minimizes at the electron mass due to a peak in the cross section with electrons and increases on either side otherwise. The sudden jump at the electron mass is due to an assumed discrete change in temperature after $e^{\pm }$ annihilation. The black region is unphysical due to DM overproduction.

Figure 5

The effective number $N_{\mathrm{eff}}$ of relativistic d.o.f. as a function of the millicharged particle mass $m_{\chi }$, assuming $N_{\nu }$ relativistic neutrinos at recombination for a Dirac fermion (DF). The solid reddish brown line is the 95% confidence level lower bound from Planck 2018. The dashed counterpart is the resulting lower bound on the millicharged particle mass for $N_{\nu }=3.046$.

Figure 6

The dark matter fraction $f$ of millicharged particles with mass $m_{\chi }$ and charge $q_{\chi }$ for Dirac fermions (DF). The region between the dashed and solid red line is the range of relic abundances that are compatible with CMB and EDGES constraints. The region above the solid grey line is ruled out due to SLAC measurements. Finally, the region to the left of the reddish brown vertical line is ruled out due to $N_{\mathrm{eff}}$ constraints. The viable regions between the SLAC and relic abundance regions have nonzero overlap, but this overlapped region does not intersect with the region permitted by $N_{\mathrm{eff}}$.

Figure 7

The dark-matter fraction $f$ of millicharged particles with mass $m_{\chi }$ and charge $q_{\chi }$ for complex scalars (CS).