Impacts of dark energy on weighing neutrinos: Mass hierarchies considered

Abstract

Taking into account the mass splittings between three active neutrinos, we investigate the impacts of dark energy on constraining the total neutrino mass $\ensuremath{\sum}{m}_{\ensuremath{\nu}}$ by using recent cosmological observations. We consider two typical dark energy models, namely, the $w\mathrm{CDM}$ model and the holographic dark energy (HDE) model, which both have an additional free parameter compared with the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ 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, the Hubble constant, and Planck lensing. Compared to the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, our study shows that the upper limit on $\ensuremath{\sum}{m}_{\ensuremath{\nu}}$ becomes much looser in the $w\mathrm{CDM}$ model but much tighter in the HDE model. In the HDE model, we obtain the 95% confidence level upper limit $\ensuremath{\sum}{m}_{\ensuremath{\nu}}<0.105\text{ }\text{ }\mathrm{eV}$ for three degenerate neutrinos. This might be the most stringent constraint on $\ensuremath{\sum}{m}_{\ensuremath{\nu}}$ by far, and it is on the verge of diagnosing the neutrino mass hierarchies in the HDE model. However, the difference of ${\ensuremath{\chi}}^{2}$ is still not significant enough to distinguish the neutrino mass hierarchies, even though the minimal ${\ensuremath{\chi}}^{2}$ of the normal hierarchy is slightly smaller than that of the inverted hierarchy.