Rapid onset of the 21-cm signal suggests a preferred mass range for dark
  matter particle
  We are approaching a new era to probe the 21-cm neutral hydrogen signal from
the period of cosmic dawn. This signal offers a unique window to the virgin
Universe, e.g., to study dark matter models with different small-scale
behaviours. The EDGES collaboration has recently published the first results of
the global 21-cm spectrum. We demonstrate that such a signal can be used to
set, unlike most observations concerning dark matter, both lower and upper
limits for the mass of dark matter particles. We study the 21-cm signal
resulting from a simple warm dark matter model with a sharp-$k$ window function
calibrated for high redshifts. We tie the PopIII star formation to Lyman-alpha
and radio background production. Using MCMC to sample the parameter space we
find that to match the EDGES signal, a warm dark matter particle must have a
mass of $7.3^{+1.6}_{-3.3}$ keV at 68\% confidence interval. This translates to
$2.2^{+1.4}_{-1.7} \times 10^{-20}$ eV for fuzzy dark matter and
$63^{+19}_{-35}$ keV for Dodelson-Widrow sterile neutrinos. Cold dark matter is
unable to reproduce the signal due to its slow structure growth.
