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