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?CDM) by using the latest cosmological observations. We consider four typical interaction forms, i.e. Q = beta H rho(de), Q = beta H rho(c), Q = beta H-0 rho(de), and Q = beta H-0 rho(c), in the I?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+Sigma m(nu) model, the constrains on Sigma m(nu), are looser in the four I Lambda CDM+Sigma m(nu) models. When considering the three mass hierarchies of neutrinos, the constraints on amn are tightest in the degenerate hierarchy case and loosest in the inverted hierarchy case. In addition, in the four I Lambda CDM+Sigma 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 1s 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+Sigma m(nu) model, the H-0 tension can be alleviated in the I Lambda CDM+Sigma m(nu) model to some extent.