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.
