Cosmological limits on neutrino unknowns versus low redshift priors

Recent Cosmic Microwave Background (CMB) temperature and polarization anisotropy measurements from the Planck mission have significantly improved previous constraints on the neutrino masses as well as the bounds on extended models with massless or massive sterile neutrino states. However, due to parameter degeneracies, additional low redshift priors are mandatory in order to sharpen the CMB neutrino bounds. We explore here the role of different priors on low redshift quantities, such as the Hubble constant, the cluster mass bias, and the reionization optical depth $\tau$. Concerning current priors on the Hubble constant and the cluster mass bias, the bounds on the neutrino parameters may differ appreciably depending on the choices adopted in the analyses. With regard to future improvements in the priors on the reionization optical depth, a value of $\tau=0.05\pm 0.01$, motivated by astrophysical estimates of the reionization redshift, would lead to $\sum m_\nu<0.0926$~eV at $90\%$~CL, when combining the full \textit{Planck} measurements, Baryon Acoustic Oscillation and Planck clusters data, thereby opening the window to unravel the neutrino mass hierarchy with existing cosmological probes.