Evidence for Massive Neutrinos from Cosmic Microwave Background and Lensing Observations

We discuss whether massive neutrinos (either active or sterile) can reconcile some of the tensions within cosmological data that have been brought into focus by the recently released Planck data. We point out that a discrepancy is present when comparing the primary CMB and lensing measurements both from the CMB and galaxy lensing data using CFHTLenS, similar to that which arises when comparing CMB measurements and SZ cluster counts. A consistent picture emerges and including a prior for the cluster constraints and BAOs we find that for an active neutrino model with three degenerate neutrinos, $\sum m_{\nu }=(0.320\pm 0.081)\mathrm{eV}$, whereas for a sterile neutrino, in addition to 3 neutrinos with a standard hierarchy and $\sum m_{\nu }=0.06\mathrm{eV}$, $m_{\nu ,\text{sterile}}^{\text{eff}}=(0.450\pm 0.124)\mathrm{eV}$ and $\mathrm{\Delta }{N}_{\text{eff}}=0.45\pm 0.23$. In both cases there is a significant detection of modification to the neutrino sector from the standard model and in the case of the sterile neutrino it is possible to reconcile the BAO and local $H_0$ measurements. However, a caveat to our result is some internal tension between the CMB and lensing and cluster observations, and the masses are in excess of those estimated from the shape of the matter power spectrum from galaxy surveys.

Figure 1

The CMB lensing power spectrum (top) data points from Planck (green squares) and SPT (blue squares) and the shear correlation function ${\xi }^{+}$ from CFHTLenS (bottom), compared to predictions for parameters from samples of the Planck $\mathrm{CMB}+\mathrm{WP}+\mathrm{BAO}\mathrm{MCMC}$ chains ($\mathrm{\Lambda }\mathrm{CDM}$, zero neutrino mass) with nonlinear corrections [18, 19]. In both cases, the data is systematically lower than theory, although the significance is somewhat lower than the eye would suggest in the case of CFHTLenS due to correlations between data points, which range from $\sim 10\%$ to $\sim 50\%$ on small and large scales, respectively. SPT data have a similar level of correlation, and for Planck the correlation is negligible.

Figure 2

Marginalized likelihoods for $\sum m_{\nu }$. The data sets are color coded in the legend, but the solid line is for (I), the dashed line is for (II), and the dotted line is for (III). It is clear that inclusion of lensing leads to a preference for $\sum m_{\nu }>0$ which is compatible with that coming from the SZ cluster counts and that there is a strong preference ($\approx 4\sigma$) in the case of data set (III).

Figure 3

Marginalized likelihoods for the sterile neutrino mass and the extra effective degrees of freedom (top and middle panels, labeling as in Fig. 2), together with the 2D joint likelihood (bottom panel).