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Neutrinos and dark energy after Planck and BICEP2: data consistency tests and cosmological parameter constraints

The detection of the B-mode polarization of the cosmic microwave background (CMB) by the BICEP2 experiment implies that the tensor-to-scalar ratio $r$ should be involved in the base standard cosmology. In this paper, we extend the $Λ$CDM+$r$+neutrino/dark radiation models by replacing the cosmological constant with the dynamical dark energy with constant $w$. Four neutrino plus dark energy models are considered, i.e., the $w$CDM+$r+\sum m_ν$, $w$CDM+r + $N_{\rm eff}$, $w$CDM+r + $\sum m_ν$ + $N_{\rm eff}$, and $w$CDM+r + $N_{\rm eff}$ + $m_{ν,{\rm sterile}}^{\rm eff}$ models. The current observational data considered in this paper include the Planck temperature data, the WMAP 9-year polarization data, the baryon acoustic oscillation data, the Hubble constant direct measurement data, the Planck Sunyaev-Zeldovich cluster counts data, the Planck CMB lensing data, the cosmic shear data, and the BICEP2 polarization data. We test the data consistency in the four cosmological models, and then combine the consistent data sets to perform joint constraints on the models. We focus on the constraints on the parameters $w$, $\sum m_ν$, $N_{\rm eff}$, and $m_{ν,{\rm sterile}}^{\rm eff}$.