Neutrinos Help Reconcile Planck Measurements with the Local Universe

Current measurements of the low and high redshift Universe are in tension if we restrict ourselves to the standard six-parameter model of flat $\mathrm{\Lambda }\mathrm{CDM}$. This tension has two parts. First, the Planck satellite data suggest a higher normalization of matter perturbations than local measurements of galaxy clusters. Second, the expansion rate of the Universe today, $H_0$, derived from local distance-redshift measurements is significantly higher than that inferred using the acoustic scale in galaxy surveys and the Planck data as a standard ruler. The addition of a sterile neutrino species changes the acoustic scale and brings the two into agreement; meanwhile, adding mass to the active neutrinos or to a sterile neutrino can suppress the growth of structure, bringing the cluster data into better concordance as well. For our fiducial data set combination, with statistical errors for clusters, a model with a massive sterile neutrino shows $3.5\sigma$ evidence for a nonzero mass and an even stronger rejection of the minimal model. A model with massive active neutrinos and a massless sterile neutrino is similarly preferred. An eV-scale sterile neutrino mass—of interest for short baseline and reactor anomalies—is well within the allowed range. We caution that (i) unknown astrophysical systematic errors in any of the data sets could weaken this conclusion, but they would need to be several times the known errors to eliminate the tensions entirely; (ii) the results we find are at some variance with analyses that do not include cluster measurements; and (iii) some tension remains among the data sets even when new neutrino physics is included.

Figure 1

Tensions between data sets and their neutrino alleviations. Black, red, and blue curves represent the $\mathrm{M}\nu \text{−}\mathrm{Md}$, $\mathrm{S}\nu \text{−}\mathrm{Md}$, and $\mathrm{S}\nu \text{−}\mathrm{Td}$ model-data combinations, respectively. Bottom: $H_0$ and $S_8$ posteriors (curves) vs local measurements (bands, 68% C.L.). Lack of overlap in $\mathrm{M}\nu \text{−}\mathrm{Md}$ is alleviated in $\mathrm{S}\nu \text{−}\mathrm{Md}$ leading to better concordance in $\mathrm{S}\nu \text{−}\mathrm{Td}$. The dashed line shows the change in $S_8$ from the 9% cluster mass offset. Top: ${\sigma }_8$ and ${\mathrm{\Omega }}_m$ 68% and 95% confidence regions. Neutrino parameters open a direction mainly orthogonal to $S_8$. $\times$ marks the ML models; $+$ shows its shift for a 9% cluster mass offset. $\mathrm{A}\nu$ model results are similar.

Figure 2

Neutrino mass and effective number constraints, labeled as in Fig. 1 ($\times$ indicates the ML model, $+$ its shift from a 9% cluster mass increase). Bottom: $\mathrm{S}\nu$ sterile case for Td (left) and Ad (right). The region excluded by the $m_s^{\mathrm{DW}}<7\mathrm{eV}$ prior is left of the dashed line. Top: $\mathrm{A}\nu$ active case for Td (left) and Ad (right). In all cases the minimal $\sum m_{\nu }=0.06\mathrm{eV}$, $N_{\text{eff}}=3.046$, and $m_s=0$ is highly excluded.