Abstract
We show that involving a sterile neutrino species in the Λ CDM + 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 Λ CDM + r + ν s model in this paper. Compared to the Λ CDM + r model, there are two extra parameters, N eff and m ν , sterile eff , in the Λ CDM + r + ν s model. We show that in this model the tension between Planck and BICEP2 can be greatly relieved at the cost of the increase of n s . However, comparing with the Λ CDM + r + d n s / d ln k 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 Λ CDM + r + ν s 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 H 0 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 Λ CDM + r + ν s model n s = 0.999 ± 0.011 , r = 0.21 − 0.05 + 0.04 , N eff = 3.95 ± 0.33 and m ν , sterile eff = 0.51 − 0.13 + 0.12 eV . Thus, our results prefer Δ N eff > 0 at the 2.7 σ level and a nonzero mass of sterile neutrino at the 3.9 σ level.
Highlights
Detection of B-mode polarization of the cosmic microwave background (CMB) was recently reported by the BICEP2 (Background Imaging of Cosmic Extragalactic Polarization) Collaboration [1]
The BICEP2 Collaboration reported the fit result of the tensor-to-scalar ratio based on the lensed-ΛCDM+r model, r = 0.20+−00..0075, from their observed B-mode power spectrum data, with r = 0 disfavored at the 7.0σ level [1]
The Planck Collaboration reported only a 95% confidence level (CL) upper limit for the tensor-to-scalar ratio, r < 0.11, from the fit to a combination of Planck, South Pole Telescope (SPT) and Atacama Cosmology Telescope (ACT) temperature data, plus the Wilkinson Microwave Anisotropy Probe (WMAP) 9-year polarization data [2]. (Note that hereafter we use highL to denote the SPT+ACT data, and use WP to denote the WMAP-9 polarization data.) there is an apparent tension between Planck and BICEP2
Summary
Detection of B-mode polarization of the cosmic microwave background (CMB) was recently reported by the BICEP2 (Background Imaging of Cosmic Extragalactic Polarization) Collaboration [1]. The BICEP2 Collaboration reported the fit result of the tensor-to-scalar ratio based on the lensed-ΛCDM+r model, r = 0.20+−00..0075, from their observed B-mode power spectrum data, with r = 0 disfavored at the 7.0σ level [1].
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