Probing the Neutrino Mass Hierarchy with Dynamical Dark Energy Model

By using a dimensionless and varies parameter $\Delta = (m_3 -m_1) / (m_3 +m_1)$, which is used to determine the neutrinos mass hierarchy, we have investigated the impacts of dark energy on the mass hierarchy. Two typical dark energy models are considered: one is the $w$CDM model with a constant equation of state parameter $w$; the other is the CPL model with a parameterized time-varying equation of state $w=w_0+ w_a(1-a)$. Adopting the currently available cosmic observations, and comparing to the $\Lambda$CDM model, our study shows that the upper limits of the total neutrino mass $\sum_\nu m_\nu$ is much looser in the $w$CDM and CPL model. In the $w$CDM (or CPL) model the total mass of neutrinos is $\sum_\nu m_\nu < 0.142$ eV (or $\sum_\nu m_\nu < 0.179$ eV) for the normal mass hierarchy and $\sum_\nu m_\nu < 0.158$ eV ($\sum_\nu m_\nu < 0.198$ eV) for the inverted mass hierarchy at $95\%$ C.L.. The $w$CDM model is slightly favored the normal mass hierarchy, but CPL model has no sympathetic to either. Furthermore, the equation of state parameters of both dark energy models can influence the measurement of $\sum_\nu m_\nu$. Larger $\sum_\nu m_\nu$ may favor phantom dark energy for $w$CDM model, and an early phantom but late quintessence dark energy for CPL model.