Constraint on neutrino masses from SDSS-III/BOSS Ly$\alpha$ forest and
  other cosmological probes
  We present constraints on the parameters of the $\Lambda$CDM cosmological
model in the presence of massive neutrinos, using the one-dimensional
Ly$\alpha$ forest power spectrum obtained with the Baryon Oscillation
Spectroscopic Survey (BOSS) of the Sloan Digital Sky Survey (SDSS) by
Palanque-Delabrouille et al. (2013), complemented by additional cosmological
probes. The interpretation of the measured Ly$\alpha$ spectrum is done using a
second-order Taylor expansion of the simulated power spectrum. BOSS
  Ly$\alpha$ data alone provide better bounds than previous Ly$\alpha$ results,
but are still poorly constraining, especially for the sum of neutrino masses
$\sum m_\nu$, for which we obtain an upper bound of 1.1~eV (95\% CL), including
systematics for both data and simulations. Ly$\alpha$ constraints on
$\Lambda$CDM parameters and neutrino masses are compatible with CMB bounds from
the Planck collaboration. Interestingly, the combination of Ly$\alpha$ with CMB
data reduces the uncertainties significantly, due to very different directions
of degeneracy in parameter space, leading to the strongest cosmological bound
to date on the total neutrino mass, $\sum m_\nu < 0.15$~eV at 95\% CL (with a
best-fit in zero). Adding recent BAO results further tightens this constraint
to $\sum m_\nu < 0.14$~eV at 95\% CL. This bound is nearly independent of the
statistical approach used, and of the different combinations of CMB and BAO
data sets considered in this paper in addition to Ly$\alpha$. Given the
measured values of the two squared mass differences $\Delta m^2$, this result
tends to favor the normal hierarchy scenario against the inverted hierarchy
scenario for the masses of the active neutrino species.
