| Summary: | We show that involving a sterile neutrino species in the ΛCDM+r model can help relieve the tension about the tensor-to-scalar ratio r between the Planck temperature data and the BICEP2 B-mode polarization data. Such a model is called the ΛCDM+r+νs model in this paper. Compared to the ΛCDM+r model, there are two extra parameters, Neff and mν,sterileeff, in the ΛCDM+r+νs model. We show that in this model the tension between Planck and BICEP2 can be greatly relieved at the cost of the increase of ns. However, comparing with the ΛCDM+r+dns/dlnk model that can significantly reduce the tension between Planck and BICEP2 but also makes trouble to inflation due to the large running of the spectral index of the order 10−2 produced, the ΛCDM+r+νs model is much better for inflation. By including a sterile neutrino species in the standard cosmology, besides the tension with BICEP2, the other tensions of Planck with other astrophysical data, such as the H0 direct measurement, the Sunyaev–Zeldovich cluster counts, and the galaxy shear data, can all be significantly relieved. So, this model seems to be an economical choice. Combining the Planck temperature data, the WMAP-9 polarization data, and the baryon acoustic oscillation data with all these astrophysical data (including BICEP2), we find that in the ΛCDM+r+νs model ns=0.999±0.011, r=0.21−0.05+0.04, Neff=3.95±0.33 and mν,sterileeff=0.51−0.13+0.12 eV. Thus, our results prefer ΔNeff>0 at the 2.7σ level and a nonzero mass of sterile neutrino at the 3.9σ level.
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