Since the B-mode polarization of the cosmic microwave background ( CMB ) was detected by the BICEP2 experiment and an unexpectedly large tensor-to-scalar ratio , r = 0.20 ^ { +0.07 } _ { -0.05 } , was found , the base standard cosmology should at least be extended to the 7-parameter \Lambda CDM+ r model .
In this paper , we consider the extensions to this base \Lambda CDM+ r model by including additional base parameters relevant to neutrinos and/or other neutrino-like relativistic components .
Four neutrino cosmological models are considered , i.e. , the \Lambda CDM+ r + \sum m _ { \nu } , \Lambda CDM+ r + N _ { eff } , \Lambda CDM+ r + \sum m _ { \nu } + N _ { eff } , and \Lambda CDM+ r + N _ { eff } + m _ { \nu, { sterile } } ^ { eff } models .
We combine the current data , including 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 , to constrain these neutrino cosmological models .
We focus on the constraints on the parameters \sum m _ { \nu } , N _ { eff } , and m _ { \nu, { sterile } } ^ { eff } .
We also discuss whether the tension on r between Planck and BICEP2 can be relieved in these neutrino cosmological models .