Constraints on neutrino mass in the scenario of vacuum energy
  interacting with cold dark matter after Planck 2018
  In this work, we investigate the constraints on the total neutrino mass in
the scenario of vacuum energy interacting with cold dark matter (abbreviated as
I$\Lambda$CDM) by using the latest cosmological observations. We consider four
typical interaction forms, i.e., $Q=\beta H \rho_{\rm de}$, $Q=\beta H
\rho_{\rm c}$, $Q=\beta H_{0} \rho_{\rm de}$, and $Q=\beta H_{0} \rho_{\rm c}$,
in the I$\Lambda$CDM scenario. To avoid the large-scale instability problem in
interacting dark energy models, we employ the extended parameterized
post-Friedmann method for interacting dark energy to calculate the perturbation
evolution of dark energy in these models. The observational data used in this
work include the cosmic microwave background (CMB) measurements from the Planck
2018 data release, the baryon acoustic oscillation (BAO) data, the type Ia
supernovae (SN) observation (Pantheon compilation), and the 2019 local distance
ladder measurement of the Hubble constant $H_{0}$ from the Hubble Space
Telescope. We find that, compared with those in the $\Lambda$CDM+$\sum m_{\nu}$
model, the constrains on $\sum m_{\nu}$ are looser in the four
I$\Lambda$CDM+$\sum m_{\nu}$ models. When considering the three mass
hierarchies of neutrinos, the constraints on $\sum m_{\nu}$ are tightest in the
degenerate hierarchy case and loosest in the inverted hierarchy case. In
addition, in the four I$\Lambda$CDM+$\sum m_{\nu}$ models, the values of
coupling parameter $\beta$ are larger using the CMB+BAO+SN+$H_{0}$ data
combination than that using the CMB+BAO+SN data combination, and $\beta>0$ is
favored at more than 1$\sigma$ level when using CMB+BAO+SN+$H_{0}$ data
combination. The issue of the $H_{0}$ tension is also discussed in this paper.
We find that, compared with the $\Lambda$CDM+$\sum m_{\nu}$ model, the $H_{0}$
tension can be alleviated in the I$\Lambda$CDM+$\sum m_{\nu}$ model to some
extent.
