In light of the recent BICEP2 B-mode polarization detection, which implies a large inflationary tensor-to-scalar ratio r0.05 = 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, H0, baryon acoustic oscillation and local cluster abundance measurements with BICEP2 data, we find the joint evidence for a sterile massive neutrino increases to ∆N eff = 0.98 ± 0.26 for the effective number and ms = 0.52 ± 0.13 eV for the effective mass or 3.8σ and 4σ 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.The recent detection of degree scale B-mode polarization in the Cosmic Microwave Background (CMB) by the BICEP2 experiment [1] implies that the inflationary ratio of tensor-to-scalar fluctuations is r 0.05 = 0.2 +0.07 −0.05 , a number in significant tension with the upper limit of r < 0.11 at 95% confidence level from the temperature anisotropy spectrum in the simplest inflationary ΛCDM cosmology [2]. This conflict occurs because the large angle temperature excess implied by the gravitational waves is not observed, and the mismatch cannot be compensated by parameter changes in this highly restricted, seven parameter model.Aside from the possibility of large astrophysical [1, 3, 4] or cosmological [5-9] foreground and systematic contamination, possible solutions include extending the inflationary side or the ΛCDM side of this model. Inflationary modifications include a large running of the scalar tilt [1]; more explicit features in the inflationary scalar spectra [10-12]; or anticorrelated isocurvature perturbations [13]. In the present work, we instead consider extensions to the matter content of the ΛCDM model that can alleviate this early Universe tension.In the ΛCDM cosmology, recall that the Planck CMB temperature anisotropy spectrum is also in conflict with * cdvorkin@ias.edu measurements of the local Universe [14][15][16]. The ΛCDM values for the current expansion rate -or Hubble constant, H 0 -and the abundance of galaxy clusters are individually in 2 − 3σ tension with direct measurements. While similar tensions existed in previous CMB data sets (e.g. [17]), the Planck results suggest a shift in the sound horizon...