Constraints on the sum of neutrino masses using cosmological data including the latest extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample

We investigate the constraints on the sum of neutrino masses ($\Sigma m_\nu$) using the most recent cosmological data, which combines the distance measurement from baryonic acoustic oscillation in the extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample with the power spectra of temperature and polarization anisotropies in the cosmic microwave background from the Planck 2015 data release. We also use other low-redshift observations including the baryonic acoustic oscillation at relatively low redshifts, the supernovae of type Ia and the local measurement of Hubble constant. In the standard cosmological constant $\Lambda$ cold dark matter plus massive neutrino model, we obtain the $95\%$ \acl{CL} upper limit to be $\Sigma m_\nu<0.129~\mathrm{eV}$ for the degenerate mass hierarchy, $\Sigma m_{\nu}<0.159~\mathrm{eV}$ for the normal mass hierarchy, and $\Sigma m_{\nu}<0.189~\mathrm{eV}$ for the inverted mass hierarchy. Based on Bayesian evidence, we find that the degenerate hierarchy is positively supported, and the current data combination can not distinguish normal and inverted hierarchies. Assuming the degenerate mass hierarchy, we extend our study to non-standard cosmological models including the generic dark energy, the spatial curvature, and the extra relativistic degrees of freedom, respectively, but find these models not favored by the data.