Lyman-alpha Forests cool Warm Dark Matter
  The free-streaming of keV-scale particles impacts structure growth on scales
that are probed by the Lyman-alpha forest of distant quasars. Using an
unprecedentedly large sample of medium-resolution QSO spectra from the ninth
data release of SDSS, along with a state-of-the-art set of hydrodynamical
simulations to model the Lyman-alpha forest in the non-linear regime, we issue
one of the tightest bounds to date, from Ly-$\alpha$ data alone, on pure dark
matter particles : $m_X > 4.09 \: \rm{keV}$ (95% CL) for early decoupled
thermal relics such as a hypothetical gravitino, and correspondingly $m_s >
24.4 \: \rm{keV}$ (95% CL) for a non-resonantly produced right-handed neutrino.
This limit depends on the value on $n_s$, and Planck measures a higher value of
$n_s$ than SDSS-III/BOSS. Our bounds thus change slightly when Ly-$\alpha$ data
are combined with CMB data from Planck 2016. The limits shift to $m_X > 2.96 \:
\rm{keV}$ (95% CL) and $m_s > 16.0 \: \rm{keV}$ (95% CL). Thanks to SDSS-III
data featuring smaller uncertainties and covering a larger redshift range than
SDSS-I data, our bounds confirm the most stringent results established by
previous works and are further at odds with a purely non-resonantly produced
sterile neutrino as dark matter.
