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 $\sum m_{\nu }$ 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 $\mathit{\text{Planck}}$~2015 data of temperature anisotropy and polarizations of Cosmic Microwave Background (CMB), we find that the $95\mathrm{\%}$ C.L. upper bounds on $\sum m_{\nu }$ refer to $\sum m_{\nu ,\mathrm{N}\mathrm{H}}<0.18$ eV for normal hierarchy (NH), $\sum m_{\nu ,\mathrm{I}\mathrm{H}}<0.20$ eV for inverted hierarchy (IH) and $\sum m_{\nu ,\mathrm{D}\mathrm{H}}<0.15$ eV for degenerate hierarchy (DH) respectively, and the normal hierarchy is slightly preferred than the inverted one ($\mathrm{\Delta }{\chi }^2\equiv {\chi }_{\mathrm{N}\mathrm{H}}^2-{\chi }_{\mathrm{I}\mathrm{H}}^2\simeq -3.4$). In addition, the additional relativistic degrees of freedom and massive sterile neutrinos are neither favored at present.