On the most constraining cosmological neutrino mass bounds
  We present here up-to-date neutrino mass limits exploiting the most recent
cosmological data sets. By making use of the Cosmic Microwave Background
temperature fluctuation and polarization measurements, Supernovae Ia luminosity
distances, Baryon Acoustic Oscillation observations and determinations of the
growth rate parameter, we are able to set the most constraining bound to date,
$\sum m_\nu<0.09$ eV at $95\%$~CL. This very tight limit is obtained without
the assumption of any prior on the value of the Hubble constant and highly
compromises the viability of the inverted mass ordering as the underlying
neutrino mass pattern in nature. The results obtained here further strengthen
the case for very large multitracer spectroscopic surveys as unique
laboratories for cosmological relics, such as neutrinos: that would be the case
of the Dark Energy Spectroscopic Instrument (DESI) survey and of the Euclid
mission.
