The linear point (LP), defined as the mid-point between the dip and the peak of the two-point clustering correlation function (TPCF), has been shown to be an excellent standard ruler for cosmology. In fact, it is nearly redshift-independent, being weakly sensitive to non-linearities, scale-dependent halo bias and redshift-space distortions. So far, these findings were tested assuming that neutrinos are massless; in this paper we extend the analysis to massive-neutrino cosmologies. In particular, we examine if the scale-dependent growth induced by neutrinos affects the LP position and if it is possible to detect the neutrino masses using the shift of the LP compared to the massless-neutrino case. For our purposes, we employ two sets of state-of-the-art $N$-body simulations with massive neutrinos. For each of them we measure the TPCF of cold dark matter (CDM) and halos and, to estimate the LP, fit the TPCF with a model-independent parametric fit in the range of scales of the Baryon Acoustic Oscillations (BAO). Overall, we find that the LP retains its features as a standard ruler even when neutrinos are massive. The cosmic distances measured with the LP can therefore be employed to constrain the neutrino mass. In addition, we propose a procedure to constrain the neutrino masses by comparing the measured LP of data to the LP of a mock galaxy catalog with massless neutrinos and fixed cosmological parameters. The small uncertainty of the LP, $\sigma_\mathrm{LP}$, plays a key role in forecasting a possible detection of neutrino masses in future surveys. We find that the sum of the neutrino masses could be detected if several redshift bins are used, provided the survey volume is sufficiently large and the shot-noise of the galaxy sample is sufficiently low.

中文翻译：

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大量中微子对相关函数线性点的影响

线性点 (LP) 定义为两点聚类相关函数 (TPCF) 的倾角和峰值之间的中点，已被证明是宇宙学的极好标准标尺。事实上，它几乎与红移无关，对非线性、与尺度相关的光晕偏差和红移空间畸变不敏感。到目前为止，这些发现是在假设中微子没有质量的情况下进行测试的。在本文中，我们将分析扩展到大质量中微子宇宙学。特别是，我们检查了由中微子引起的尺度依赖性增长是否会影响 LP 位置，以及与无质量中微子情况相比，是否可以使用 LP 的位移来检测中微子质量。出于我们的目的，我们采用了两组最先进的具有大量中微子的 $N$ 体模拟。对于它们中的每一个，我们测量冷暗物质 (CDM) 和光晕的 TPCF，并且为了估计 LP，在重子声学振荡 (BAO) 的尺度范围内使用与模型无关的参数拟合来拟合 TPCF。总的来说，我们发现即使中微子质量很大，LP 仍保留其作为标准尺的特征。因此，可以使用 LP 测量的宇宙距离来约束中微子质量。此外，我们提出了一种程序，通过将测量的数据 LP 与具有无质量中微子和固定宇宙学参数的模拟星系目录的 LP 进行比较，来限制中微子质量。LP 的小不确定性 $\sigma_\mathrm{LP}$ 在预测未来调查中可能检测到中微子质量方面起着关键作用。