  The most recent measurements of the temperature and low-multipole
polarization anisotropies of the Cosmic Microwave Background (CMB) from the
Planck satellite, when combined with galaxy clustering data from the Baryon
Oscillation Spectroscopic Survey (BOSS) in the form of the full shape of the
power spectrum, and with Baryon Acoustic Oscillation measurements, provide a
$95\%$ confidence level (CL) upper bound on the sum of the three active
neutrinos $\sum m _\nu< 0.183$ eV, among the tightest neutrino mass bounds in
the literature, to date, when the same datasets are taken into account. This
very same data combination is able to set, at $\sim70\%$ CL, an upper limit on
$\sum m _\nu$ of $0.0968$ eV, a value that approximately corresponds to the
minimal mass expected in the inverted neutrino mass hierarchy scenario. If
high-multipole polarization data from Planck is also considered, the $95\%$ CL
upper bound is tightened to $\sum m _\nu< 0.176$ eV. Further improvements are
obtained by considering recent measurements of the Hubble parameter. These
limits are obtained assuming a specific non-degenerate neutrino mass spectrum;
they slightly worsen when considering other degenerate neutrino mass schemes.
Current cosmological data, therefore, start to be mildly sensitive to the
neutrino mass ordering. Low-redshift quantities, such as the Hubble constant or
the reionization optical depth, play a very important role when setting the
neutrino mass constraints. We also comment on the eventual shifts in the
cosmological bounds on $\sum m_\nu$ when possible variations in the former two
quantities are addressed.
