Early-Universe constraints on dark matter-baryon scattering and their implications for a global 21 cm signal

We present and compare several cosmological constraints on the cross section for elastic scattering between dark matter (DM) and baryons, for cross sections with a range of power-law dependences on the DM-baryon relative velocity $v$, especially focusing on the case of $\sigma \propto v^{-4}$. We study constraints spanning a wide range of epochs in cosmological history, from prerecombination distortions to the blackbody spectrum and anisotropies of the cosmic microwave background (CMB), to modifications to the intergalactic medium temperature and the resulting 21 cm signal, and discuss the allowed signals in the latter channels given the constraints from the former. We improve previous constraints on DM-baryon scattering from the CMB anisotropies, demonstrate via principal component analysis that the effect on the CMB can be written as a simple function of DM mass for $v^{-4}$ scattering, and map out the redshifts dominating this signal. We show that given high-redshift constraints on DM-baryon scattering, a $v^{-4}$ scaling of the cross section for light DM would be sufficient to explain the deep 21 cm absorption trough recently claimed by the Experiment to Detect the Reionization Step, if 100% of the DM scatters with baryons; we estimate the minimal necessary velocity scaling and find that it is close to $v^{-4}$. For millicharged DM models proposed to explain the observation, where only a small fraction of the DM interacts, we estimate that a PIXIE-like future experiment measuring CMB spectral distortion could test the relevant parameter space.

Figure 1

95% confidence upper limits on the DM-baryon scattering cross section $\sigma ={\sigma }_0{v}^n$, computed using MontePython, for (upper panel) $n=0$ and (lower panel) $n=-4$. For black solid lines labeled “Planck” the Planck 2015 TTTEEE likelihood is employed; for blue dashed lines labeled “ACT/SPT” the 2013 ACT and SPT likelihoods are added. Dots indicate MCMC results. In the upper panel, these dots are joined by straight lines; in the lower panel, the line follows the ${\sigma }_0\propto 1+m_{\chi }/m_H$ scaling suggested in Ref. [5].

Figure 2

The change in the temperature power spectrum up to $\ell =5000$, assuming a DM mass of 0.1 GeV, with a cross section given by the “Planck” upper limit in Fig. 1.

Figure 3

Change of the CMB temperature power spectrum at $\ell =100$, 1500, 3000 as a function of the DM-baryon scattering cross section, for a DM mass of 0.1 GeV; cosmological parameters are held fixed at the $\mathrm{\Lambda }\mathrm{CDM}$ values.

Figure 4

The effect on the CMB temperature power spectrum of turning on DM-baryon scattering in a narrow redshift range about $10^3$ (green line), $10^4$ (red line), and at both redshifts (black dashed line). The cross section is set to ${\sigma }_0=2\times {10}^{-41}({\mathrm{cm}}^2)$ for $z={10}^3$ and ${\sigma }_0={10}^{-41}({\mathrm{cm}}^2)$ for $z={10}^4$, and in both cases $\sigma ={\sigma }_0{v}^{-4}$ scaling is assumed. The sum of the red and green lines is shown as the blue line; to the degree that the problem is linear, the blue line should overlap the black dashed line.

Figure 5

Relative significance of isolated scattering at different redshifts, estimated using the Fisher-matrix analysis detailed in the text, for DM masses 10 keV (solid black line, lower panel only), 0.1 GeV (dashed blue line) and 1 TeV (dotted red line), for $n=0$ (upper panel) and $n=-4$ (lower panel).

Figure 6

Principal components ($\mathrm{first}=\text{thick}$, blue; $\mathrm{second}=\text{medium}$, red; $\mathrm{third}=\text{thin}$, green) for 0.1 GeV DM with redshift-dependent scattering, for $n=0$ and $n=-4$, overlaid with the significance curves of Fig. 5.

Figure 7

First principal component (arbitrary normalization) as a function of the DM mass, for $n=0$ scattering (solid black line) and $n=-4$ scattering (dashed blue line). We also overplot the simple mass scaling suggested in Ref. [5].

Figure 8

Comparison between the MCMC-based constraints (the solid black line is calculated with the Planck likelihoods, and the dashed blue line is calculated with ACT/SPT) on the scattering cross section as a function of DM mass, for two different choices of the velocity dependence of scattering, with the forecast sensitivity from a Fisher analysis for a Planck-like experiment (dot-dashed red line). We also show the predicted sensitivity of a future idealized experiment that is CVL up to ${\ell }_{\max }=5000$ (dotted green line). For $n=-4$ we also show the Fisher-forecast sensitivity for a Planck-like experiment under the assumption $V_{\mathrm{rms}}=0$ (dot-dashed purple line), labeled by ${\mathrm{PCA}}_0$.

Figure 9

Example temperature evolution for baryons (blue) and DM (red) with (dashed) and without (solid) $n=-4$ DM-baryon scattering. The DM mass is taken to be 0.1 GeV, and the cross section is chosen to saturate the CMB-anisotropy limit derived in Sec. 3.

Figure 10

Maximum allowed change in baryon temperature due to DM-baryon scattering with $n=0$ (blue) and $n=-4$ (red), scanning over keV–TeV DM masses. For each mass, the cross section is taken to saturate the CMB anisotropy limit derived in Sec. 3 (using both Planck and ACT/SPT data). The dark red band shows the range of maximum temperature modifications for sub-GeV DM masses, whereas the light red band covers the mass range up to 1 TeV. The black region shows the minimum gas temperature change, relative to the $\mathrm{\Lambda }\mathrm{CDM}$ baseline, preferred by the recent measurement by EDGES (95% confidence region) [7]. The purple region labeled by $n_0=-4$ corresponds to the temperature shift from scattering of sub-GeV DM with the assumption $V_{\mathrm{rms}}=0$, assuming the cross section saturates the limit labeled by ${\mathrm{PCA}}_0$ in Fig. 8.

Figure 11

Maximum allowed change in baryon temperature at $z=17$ (blue) due to DM-baryon scattering, with cross sections saturating Fisher estimates of current bounds from the CMB, as a function of $n$. The red line indicates the gas temperature modification needed to match the central value of the recent EDGES measurement of 21 cm absorption.

Figure 12

Change of baryon temperature with redshift for $n=-4$, for three different calculations of the DM-baryon relative velocity evolution: the mean-field approach (black solid), and evolving $V_{\chi ,b}$ with two initial conditions for $V_{\chi b,0}$ (blue dashed and red dotted). The DM mass is set to be 0.1 GeV, and the cross section saturates the CMB-anisotropy limit.

Figure 13

IGM limit for different velocity-dependent cross sections assuming current sensitivity of Lyman-$\alpha$ forest data.

Figure 14

Estimated cross section limit from spectral distortion constraints for $n=0$ and $n=-4$ scattering, assuming FIRAS (solid line) or PIXIE (dashed line) sensitivity, using the analytic solution in Ref. [6] (black), and the numerical results of this work (blue).

Figure 15

Preferred parameters for millicharged DM to explain the EDGES 21 cm absorption detection [9] (black line) with 1% of the DM being millicharged, and the estimated sensitivity of experiments to measure spectral distortion, calculated in this work. The dashed blue line reflects current constraints (FIRAS) whereas the dotted red line corresponds to a future PIXIE-like experiment with sensitivity to ${10}^{-8}$ distortions.