Sterile neutrinos help reconcile the observational results of primordial gravitational waves from Planck and BICEP2

Abstract

We show that involving a sterile neutrino species in the $\Lambda$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 $\Lambda$CDM+$r$+${\nu }_s$ model in this paper. Compared to the $\Lambda$CDM+$r$ model, there are two extra parameters, $N_{\mathrm{eff}}$ and $m_{\nu ,\mathrm{sterile}}^{\mathrm{eff}}$, in the $\Lambda$CDM+$r$+${\nu }_s$ 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 $\Lambda$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 order $10^{-2}$ produced, the $\Lambda$CDM+$r$+${\nu }_s$ 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 $\Lambda$CDM+$r$+${\nu }_s$ model $n_s=0.999\pm 0.011$, $r=0.21_{-0.05}^{+0.04}$, $N_{\mathrm{eff}}=3.95\pm 0.33$ and $m_{\nu ,\mathrm{sterile}}^{\mathrm{eff}}=0.51_{-0.13}^{+0.12}$ eV. Thus, our results prefer $\Delta N_{\mathrm{eff}}>0$ at the 2.7$\sigma$ level and a nonzero mass of sterile neutrino at the 3.9$\sigma$ level.

5 pages, 3 figures

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