Unveiling $\nu$ secrets with cosmological data: neutrino masses and mass hierarchy.

Using some of the latest cosmological datasets publicly available, we derive the strongest bounds in the literature on the sum of the three active neutrino masses, $M_\nu$, within the assumption of a background flat $\Lambda$CDM cosmology. In the most conservative scheme, combining Planck cosmic microwave background (CMB) temperature anisotropies and baryon acoustic oscillations (BAO) data, as well as the up-to-date constraint on the optical depth to reionization ($\tau$), the tightest $95\%$ confidence level (C.L.) upper bound we find is $M_\nu<0.151$~eV. The addition of Planck high-$\ell$ polarization data, which however might still be contaminated by systematics, further tightens the bound to $M_\nu<0.118$~eV. A proper model comparison treatment shows that the two aforementioned combinations disfavor the IH at $\sim 64\%$~C.L. and $\sim 71\%$~C.L. respectively. In addition, we compare the constraining power of measurements of the full-shape galaxy power spectrum versus the BAO signature, from the BOSS survey. Even though the latest BOSS full shape measurements cover a larger volume and benefit from smaller error bars compared to previous similar measurements, the analysis method commonly adopted results in their constraining power still being less powerful than that of the extracted BAO signal. Our work uses only cosmological data; imposing the constraint $M_\nu>0.06\,{\rm eV}$ from oscillations data would raise the quoted upper bounds by ${\cal O}(0.1\sigma)$ and would not affect our conclusions.