Update constraints on neutrino mass and mass hierarchy in light of dark energy models

Combining cosmic microwave background (CMB) data from Planck satellite data, Baryon Acoustic Oscillations (BAO) measurements and Type Ia supernovae (SNe Ia) data, we obtain the bounds on total neutrino masses $M_ u$ with the approximation of degenerate neutrino masses and for three dark energy models: the cosmological constant ($Lambda$CDM) model, a phenomenological emergent dark energy (PEDE) model and a model-independent quintessential parameterization (HBK). The bounds on the sum of neutrino masses $M_ u$ depend on the dark energy (DE) models. In the HBK model, we confirm the conclusion from some previous work that the quintessence prior of dark energy tends to tighten the cosmological constraint on $M_ u$. On the other hand, the PEDE model leads to larger $M_ u$ and a nonzero lower bound. Besides, we also explore the correlation between three different neutrino hierarchies and dark energy models.