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 $\Lambda$CDM), i.e.,
the $w$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 $\sum m_\nu$
and $H_0$ will be changed, i.e., in the $\Lambda$CDM model, $\sum m_\nu$ is
anti-correlated with $H_0$, but in the $w$CDM and HDE models, $\sum m_\nu$
becomes positively correlated with $H_0$. Compared to $\Lambda$CDM, in the
$w$CDM model the limit on $\sum m_\nu$ becomes much looser, but in the HDE
model the limit becomes much tighter. In the HDE model, we obtain $\sum
m_\nu<0.113$ eV ($95\%$ CL) 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.
