No New Cosmological Concordance with Massive Sterile Neutrinos

It has been claimed recently that massive sterile neutrinos could bring about a new concordance between observations of the cosmic microwave background, the large-scale structure of the Universe, and local measurements of the Hubble constant, $H_0$. We demonstrate that this apparent concordance results from combining data sets which are in significant tension, even within this extended model, possibly indicating remaining systematic biases in the measurements. We further show that this tension remains when the cosmological model is further extended to include significant tensor modes, as suggested by the recent BICEP2 results. Using the Bayesian evidence, we show that the cold dark matter model with a cosmological constant is strongly favored over its neutrino extensions by various combinations of data sets. Robust data combinations yield stringent limits of $\sum m_{\nu }\lesssim 0.3\mathrm{eV}$ and $m_{\nu ,\text{sterile}}^{\text{eff}}\lesssim 0.3\mathrm{eV}$ at 95% C.L. for the sum of active and sterile neutrinos, respectively.

Figure 1

Constraints on the $\mathrm{\Lambda }\mathrm{CDM}+{\mathrm{N}}_{\text{eff}}+m_{\nu ,\text{sterile}}^{\text{eff}}$ model, showing that nonzero sterile neutrino mass is only favored as a result of a tension between the CMB and cluster data (PlaSZ, Xray) in the ${\sigma }_8-{\mathrm{\Omega }}_m$ plane, and the degeneracy between ${\sigma }_8$ and neutrino mass.

Figure 2

Persistence of the tension as the minimal $\mathrm{\Lambda }\mathrm{CDM}$ model is extended in the neutrino sector, i.e., as ${\mathrm{N}}_{\text{eff}}$ and massive active or sterile neutrinos are added.

Figure 3

Constraints on the $\mathrm{\Lambda }\mathrm{CDM}+r_{0.002}+{\mathrm{N}}_{\text{eff}}+m_{\nu ,\text{sterile}}^{\text{eff}}$ model, illustrating the persisting tension between x-ray clusters and $\mathrm{CMB}+\mathrm{BAO}$ in the ${\sigma }_8-{\mathrm{\Omega }}_m$ plane, despite an apparent reconciliation of the BICEP and Planck results on $r_{0.002}$.