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, $\sum m_{\nu }<0.09\mathrm{eV}$ at 95% C.L. 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 survey and of the Euclid mission.

• Received 26 July 2021
• Accepted 27 August 2021

DOI:https://doi.org/10.1103/PhysRevD.104.083504