Critical look at the cosmological neutrino mass bound

Cosmological neutrino mass bounds are becoming increasingly stringent. The latest limit within ΛCDM from Planck 2018+ACT lensing+DESI is ∑mν<0.072 eV at 95% CL, very close to the minimum possible sum of neutrino masses (∑mν>0.06 eV), hinting at vanishing or even "negative"cosmological neutrino masses. In this context, it is urgent to carefully evaluate the origin of these cosmological constraints. In this paper, we investigate the robustness of these results in three ways: (i) we check the role of potential anomalies in Planck CMB and DESI BAO data; (ii) we compare the results for frequentist and Bayesian techniques, as very close to physical boundaries subtleties in the derivation and interpretation of constraints can arise; (iii) we investigate how deviations from ΛCDM, potentially alleviating these anomalies, can alter the constraints. From a profile likelihood analysis, we derive constraints in agreement at the ∼10% level with Bayesian posteriors. We find that the weak preference for negative neutrino masses is mostly present for Planck 18 data, affected by the well-known "lensing anomaly."It disappears when the new Planck 2020 HiLLiPoP is used, leading to significantly weaker constraints. Additionally, the pull toward negative masses in DESI data stems from the z=0.7 bin, which contains a BAO measurement in ∼3σ tension with Planck expectations. Without this bin, and in combination with HiLLiPoP, the bound relaxes to ∑mν<0.11 eV at 95% CL. The recent preference for dynamical dark energy alleviates this tension and further weakens the bound. As we are at the dawn of a neutrino mass discovery from cosmology, it will be very exciting to see if this trend is confirmed by future data.