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.

中文翻译：

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普朗克 2018 之后真空能量与冷暗物质相互作用情景中中微子质量的约束

在这项工作中，我们利用最新的宇宙学观测研究了真空能量与冷暗物质相互作用的情景（缩写为 I$\Lambda$CDM）对中微子总质量的约束。我们考虑四种典型的交互形式，即$Q=\beta H \rho_{\rm de}$, $Q=\beta H \rho_{\rm c}$, $Q=\beta H_{0} \rho_ {\rm de}$ 和 $Q=\beta H_{0} \rho_{\rm c}$，在 I$\Lambda$CDM 场景中。为了避免相互作用暗能量模型中的大规模不稳定问题，我们采用扩展参数化后弗里德曼相互作用暗能量方法来计算这些模型中暗能量的扰动演化。这项工作中使用的观测数据包括普朗克 2018 年数据发布的宇宙微波背景 (CMB) 测量值、重子声学振荡 (BAO) 数据、Ia 型超新星 (SN) 观测（万神殿汇编），以及来自哈勃太空望远镜的哈勃常数 $H_{0}$ 的 2019 年局部距离阶梯测量。我们发现，与$\Lambda$CDM+$\sum m_{\nu}$模型相比，$\sum m_{\nu}$的约束在四个I$\Lambda$CDM+$\总和 m_{\nu}$ 模型。在考虑中微子的三个质量层次时，对 $\sum m_{\nu}$ 的约束在退化层次情况下最严格，在倒层次情况下最松。此外，在四个 I$\Lambda$CDM+$\sum m_{\nu}$ 模型中，使用 CMB+BAO+SN+$H_{0}$ 数据组合的耦合参数 $\beta$ 的值大于使用CMB+BAO+SN数据组合，并且当使用CMB+BAO+SN+$H_{0}$数据组合时，$\beta>0$在超过1$\sigma$级别受到青睐。本文还讨论了 $H_{0}$ 张力的问题。我们发现，与 $\Lambda$CDM+$\sum m_{\nu}$ 模型相比，$H_{0}$ 的张力可以在 I$\Lambda$CDM+$\sum m_{\nu} 中得到缓解$ 模型在某种程度上。