标题： 暗能量对测量中微子质量的影响：考虑质量顺序 显示英文标题

标题： Impacts of dark energy on weighing neutrinos: mass hierarchies considered

摘要： 考虑到三种活性中微子之间的质量分裂，我们通过最近的宇宙学观测研究了暗能量对约束总中微子质量$\sum m_{\nu}$的影响。我们考虑了两种典型的暗能量模型，即$w$CDM 模型和全息暗能量（HDE）模型，这两种模型相比$\Lambda$CDM 模型都多了一个自由参数。我们使用了普朗克 2015 年的 CMB 温度和极化各向异性数据，结合低红移的 BAO 距离尺度测量、Ia 型超新星、哈勃常数和普朗克引力透镜数据。与$\Lambda$CDM 模型相比，我们的研究显示，在$w$CDM 模型中，对$\sum m_{\nu}$的上限变得宽松得多，而在 HDE 模型中则变得更为严格。 在HDE模型中，我们得到三个简并中微子的$95\%$CL上限$\sum m_{\nu}<0.105~\textrm{eV}$。 这可能是迄今为止对$\sum m_{\nu}$最严格的约束，并几乎接近于在HDE模型中诊断中微子质量层次。 然而，$\chi^2$的差异仍然不够显著，无法区分中微子质量层次，尽管正常层次的最小$\chi^2$略小于反常层次的值。 显示英文摘要

摘要： Taking into account the mass splittings between three active neutrinos, we investigate impacts of dark energy on constraining the total neutrino mass $\sum m_{\nu}$ by using recent cosmological observations. We consider two typical dark energy models, namely, the $w$CDM model and the holographic dark energy (HDE) model, which both have an additional free parameter compared with the $\Lambda$CDM model. We employ the Planck 2015 data of CMB temperature and polarization anisotropies, combined with low-redshift measurements on BAO distance scales, type Ia supernovae, Hubble constant, and Planck lensing. Compared to the $\Lambda$CDM model, our study shows that the upper limit on $\sum m_{\nu}$ becomes much looser in the $w$CDM model while much tighter in the HDE model. In the HDE model, we obtain the $95\%$ CL upper limit $\sum m_{\nu}<0.105~\textrm{eV}$ for three degenerate neutrinos. This might be the most stringent constraint on $\sum m_{\nu}$ by far and is almost on the verge of diagnosing the neutrino mass hierachies in the HDE model. However, the difference of $\chi^2$ is still not significant enough to distinguish the neutrino mass hierarchies, even though the minimal $\chi^2$ of the normal hierarchy is slightly smaller than that of the inverted hierarchy.