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Constraints on the neutrino mass and mass hierarchy from cosmological observations

Considering the mass splitting between three active neutrinos, we represent the new constraints on the sum of neutrino mass $\sum m_ν$ by updating the anisotropic analysis of Baryon Acoustic Oscillation (BAO) scale in the CMASS and LOWZ galaxy samples from Data Release 12 of the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS DR12). Combining the BAO data of 6dFGS, MGS, LOWZ and CMASS with $\textit{Planck}$~2015 data of temperature anisotropy and polarizations of Cosmic Microwave Background (CMB), we find that the $95\%$ C.L. upper bounds on $\sum m_ν$ refer to $\sum m_{ν,\rm NH}<0.18$ eV for normal hierarchy (NH), $\sum m_{ν,\rm IH}<0.20$ eV for inverted hierarchy (IH) and $\sum m_{ν,\rm DH}<0.15$ eV for degenerate hierarchy (DH) respectively, and the normal hierarchy is slightly preferred than the inverted one ($Δχ^2\equiv χ^2_{\rm NH}-χ^2_{\rm IH} \simeq -3.4$). In addition, the additional relativistic degrees of freedom and massive sterile neutrinos are neither favored at present.