In light of the recent BICEP2 B-mode polarization detection, which implies a large inflationary tensor-to-scalar ratio r_{0.05}=0.2^{+0.07}_{-0.05}, we re-examine the evidence for an extra sterile massive neutrino, originally invoked to account for the tension between the cosmic microwave background (CMB) temperature power spectrum and local measurements of the expansion rate H0 and cosmological structure. With only the standard active neutrinos and power-law scalar spectra, this detection is in tension with the upper limit of r<0.11 (95% confidence) from the lack of a corresponding low multipole excess in the temperature anisotropy from gravitational waves. An extra sterile species with the same energy density as is needed to reconcile the CMB data with H0 measurements can also alleviate this new tension. By combining data from the Planck and ACT/SPT temperature spectra, WMAP9 polarization, H_0, baryon acoustic oscillation and local cluster abundance measurements with BICEP2 data, we find the joint evidence for a sterile massive neutrino increases to DeltaNeff=0.98pm 0.26 for the effective number and ms= 0.52pm 0.13 eV for the effective mass or 3.8 sigma and 4 sigma evidence respectively. We caution the reader that these results correspond to a joint statistical evidence and, in addition, astrophysical systematic errors in the clusters and H0 measurements, and small-scale CMB data could weaken our conclusions.
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