Impacts of dark energy on weighing neutrinos: mass hierarchies   considered
  Taking into account the mass splittings between three active neutrinos, we investigate impacts of dark energy on constraining the total neutrino mass $\sum m_{\nu}$ by using recent cosmological observations. We consider two typical dark energy models, namely, the $w$CDM model and the holographic dark energy (HDE) model, which both have an additional free parameter compared with the $\Lambda$CDM model. We employ the Planck 2015 data of CMB temperature and polarization anisotropies, combined with low-redshift measurements on BAO distance scales, type Ia supernovae, Hubble constant, and Planck lensing. Compared to the $\Lambda$CDM model, our study shows that the upper limit on $\sum m_{\nu}$ becomes much looser in the $w$CDM model while much tighter in the HDE model. In the HDE model, we obtain the $95\%$ CL upper limit $\sum m_{\nu}<0.105~\textrm{eV}$ for three degenerate neutrinos. This might be the most stringent constraint on $\sum m_{\nu}$ by far and is almost on the verge of diagnosing the neutrino mass hierachies in the HDE model. However, the difference of $\chi^2$ is still not significant enough to distinguish the neutrino mass hierarchies, even though the minimal $\chi^2$ of the normal hierarchy is slightly smaller than that of the inverted hierarchy. 
Sai Wang, Yi-Fan Wang, Dong-Mei Xia, Xin Zhang
astro-ph.CO gr-qc hep-ph