  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 $5.3 \times 10^{-27}$ cm$^2$ for 1 keV, $3.0 \times 10^{-26}$ cm$^2$ for 1
MeV, $1.7 \times 10^{-25}$ cm$^2$ for 1 GeV, and $1.6 \times 10^{-23}$ cm$^2$
for 1 TeV dark matter mass. Finally, we discuss the implications of this study
for dark matter physics and future observations.
