红移空间畸变对宇宙物质密度场持续同调的影响
Impact of Redshift Space Distortion on Persistent Homology of cosmic matter density field
AI总结：
本研究利用持续同调统计量，分析了红移空间畸变对三维物质密度场偏移集拓扑的影响，发现约化Betti数对RSD和平滑尺度表现出不同的敏感性，且持续熵是抵御非线性影响的可靠度量。
摘要：
通过采用从持续同调（PH）获得的统计量，我们研究了红移空间畸变（RSD）对超水平过滤方法应用于三维物质密度场形成的偏移集拓扑结构的影响。由 Quijote 套件在真实空间和红移空间中模拟的合成场，通过考虑不同尺度的高斯平滑函数进行了平滑处理。RSD 导致星系团（$\tildeβ_0$）向更高阈值移动的趋势，而纤维环（$\tildeβ_1$）和宇宙空洞（$\tildeβ_2$）则向更低阈值迁移。值得注意的是，与星系团和独立环相比，$\tildeβ_2$ 对 RSD 表现出更高的敏感性。随着平滑尺度的增加，约化 Betti 数曲线（$\tildeβ_k$）的幅度减小，相应的峰值位置向平均阈值移动。相反，对于 $z\in[0-3]$ 的红移变化，$\tildeβ_k$ 的幅度几乎保持不变。对持续熵和 $k$-holes 总体丰度的分析表明，在 $z=0$ 时对于 $R \gtrsim 30$ Mpc $h^{-1}$，线性 Kaiser 效应比非线性效应起着更重要的作用，而持续熵被证明是抵御非线性影响的可靠度量。
英文摘要：
By employing summary statistics obtained from Persistent Homology (PH), we investigate the influence of Redshift Space Distortions (RSD) on the topology of excursion sets formed through the super-level filtration method applied to three-dimensional matter density fields. The synthetic fields simulated by the Quijote suite in both real and redshift spaces are smoothed by accounting for the Gaussian smoothing function with different scales. The RSD leads a tendency for clusters ($\tildeβ_0$) to shift towards higher thresholds, while filament loops ($\tildeβ_1$) and cosmic voids ($\tildeβ_2$) migrate towards lower thresholds. Notably, $\tildeβ_2$ exhibits greater sensitivity to RSD compared to clusters and independent loops. As the smoothing scales increase, the amplitude of the reduced Betti number curve ($\tildeβ_k$) decreases, and the corresponding peak position shifts towards the mean threshold. Conversely, the amplitude of $\tildeβ_k$ remains almost unchanged with variations in redshift for $z\in[0-3]$. The analysis of persistent entropy and the overall abundance of $k$-holes indicates that the linear Kaiser effect plays a significant role compared to the non-linear effect for $R \gtrsim 30$ Mpc $h^{-1}$ at $z=0$, whereas persistent entropy proves to be a reliable measure against non-linear influences.
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