Constraints on Scattering of keV–TeV Dark Matter with Protons in the Early Universe

We present the first cosmological constraint on dark matter scattering with protons in the early Universe for the entire range of dark matter masses between 1 keV and 1 TeV. This constraint is derived from the Planck measurements of the cosmic microwave background (CMB) temperature and polarization anisotropy, and the CMB lensing anisotropy. It improves upon previous CMB constraints by many orders of magnitude, where limits are available, and closes the gap in coverage for low-mass dark matter candidates. We focus on two canonical interaction scenarios: spin-independent and spin-dependent scattering with no velocity dependence. Our results exclude (with 95% confidence) spin-independent interactions with cross sections greater than $5.3\times {10}^{-27}{\mathrm{cm}}^2$ for 1 keV, $3.0\times {10}^{-26}{\mathrm{cm}}^2$ for 1 MeV, $1.7\times {10}^{-25}{\mathrm{cm}}^2$ for 1 GeV, and $1.6\times {10}^{-23}{\mathrm{cm}}^2$ for 1 TeV dark matter mass. Finally, we discuss the implications of this study for dark matter physics and future observations.

Figure 1

Constraints on the DM-proton scattering cross section, as derived from various cosmological measurements; shaded regions are excluded with 95% confidence. The exclusion curves that partially span this mass range are from previous state-of-the-art results, while the red curves that span the entire mass range represent the constraints derived in this study for spin-independent and spin-dependent scattering.

Figure 2

Percent difference in the CMB temperature power spectrum between the $\mathrm{\Lambda }\mathrm{CDM}$ model and a model with spin-independent DM-proton scattering, where the interaction strength is set to its 95% confidence-level upper limit (while all other cosmological parameters are kept at their best-fit Planck 2015 values [51]). The size of Planck $2\sigma$ error bar (binned with a bin size $\mathrm{\Delta }\ell =50$) is roughly represented by the shaded region, for reference. Note that most of Planck’s constraining power comes from the smallest well-measured angular scale at $\ell \sim 1200$; roughly speaking, this implies that our reported constraint is most sensitive to DM scattering at a redshift corresponding to the horizon entry of the smallest measurable mode that has experienced scattering with baryons for the longest time.