Impacts of dark energy on weighing neutrinos after Planck 2015

We investigate how dark energy properties impact the cosmological limits on the total mass of active neutrinos. We consider two typical, simple dark energy models (that have only one more additional parameter than $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$), i.e., the $w\mathrm{CDM}$ model and the holographic dark energy (HDE) model, as examples, to make an analysis. In the cosmological fits, we use the Planck 2015 temperature and polarization data, in combination with other low-redshift observations, including the baryon acoustic oscillations, type Ia supernovae, and Hubble constant measurement, as well as the Planck lensing measurements. We find that, once dynamical dark energy is considered, the degeneracy between $\ensuremath{\sum}{m}_{\ensuremath{\nu}}$ and ${H}_{0}$ will be changed, i.e., in the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, $\ensuremath{\sum}{m}_{\ensuremath{\nu}}$ is anticorrelated with ${H}_{0}$, but in the $w\mathrm{CDM}$ and HDE models, $\ensuremath{\sum}{m}_{\ensuremath{\nu}}$ becomes positively correlated with ${H}_{0}$. Compared to $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$, in the $w\mathrm{CDM}$ model the limit on $\ensuremath{\sum}{m}_{\ensuremath{\nu}}$ becomes much looser, but in the HDE model the limit becomes much tighter. In the HDE model, we obtain $\ensuremath{\sum}{m}_{\ensuremath{\nu}}<0.113\text{ }\text{ }\mathrm{eV}$ (95% C.L.) with the combined data sets, which is perhaps the most stringent upper limit by far on neutrino mass. Thus, our result in the HDE model is nearly ready to diagnose the neutrino mass hierarchy with the current cosmological observations.