Neutrino constraints: what large-scale structure and CMB data are telling us?

We discuss the reliability of neutrino mass constraints, either active or sterile, from the combination of different low redshift Universe probes with measurements of CMB anisotropies. In our analyses we consider WMAP 9-year or Planck Cosmic Microwave Background (CMB) data in combination with Baryonic Acoustic Oscillations (BAO) measurements from BOSS DR11, galaxy shear measurements from CFHTLenS, SDSS Ly-a forest constraints and galaxy cluster mass function from Chandra observations. At odds with recent similar studies, to avoid model dependence of the constraints we perform a full likelihood analysis for all the datasets employed. As for the cluster data analysis we rely on to the most recent calibration of massive neutrino effects in the halo mass function and we explore the impact of the uncertainty in the mass bias and re-calibration of the halo mass function due to baryonic feedback processes on cosmological parameters. We find that none of the low redshift probes alone provide evidence for massive neutrino in combination with CMB measurements, while a larger than 2 sigma detection of non zero neutrino mass, either active or sterile, is achieved combining cluster or shear data with CMB and BAO measurements. Yet, the significance of the detection exceeds 3 sigma if we combine all four datasets. For a three active neutrino scenario, from the joint analysis of CMB, BAO, shear and cluster data including the uncertainty in the mass bias we obtain Sigma m(nu) = 0.29(-0.21)(+0.18) eV and Sigma m(nu) = 0.22(-0.18)(+0.17) eV (95%CL) using WMAP9 or Planck as CMB dataset, respectively. The preference for massive neutrino is even larger in the sterile neutrino scenario, for which we get m(s)(eff) = 0.44(-0.26)(+0.28) eV and Delta N-eff = 0.78(-0.59)(+0.60) = (95%CL) from the joint analysis of Planck, BAO, shear and cluster datasets. For this data combination the vanilla Lambda CDM model is rejected at more than 3 sigma and a sterile neutrino mass as motivated by accelerator anomaly is within the 2 sigma errors. Conversely, the Ly-alpha data favour vanishing neutrino masses and from the data combination Planck+BAO+Ly-alpha we get the tight upper limits Sigma m(nu) < 0.14 eV and m(s)(eff) < 0.22 eV - Delta N-eff < 1.11 (95%CL) for the active and sterile neutrino model, respectively. Finally, results from the full data combination reflect the tension between the sigma(8) constraints obtained from cluster and shear data and that inferred from Ly-alpha forest measurements; in the active neutrino scenario for both CMB datasets employed, the full data combination yields only an upper limits on Sigma m(nu), while assuming an extra sterile neutrino we still get preference for non-vanishing mass, m(s)(eff) = 0.26(-0.24)(+0.22) eV, and dark contribution to the radiation content, Delta N-eff = 0.82 +/- 0.55.