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arXiv · 2410.01751

Impact of Redshift Space Distortion on Persistent Homology of cosmic matter density field

Fatemeh Abedi·Mohammad Hossein Jalali Kanafi·S. M. S. Movahed
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Abstract

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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Fatemeh Abedi, Mohammad Hossein Jalali Kanafi, S. M. S. Movahed. 2025-03-03. Impact of Redshift Space Distortion on Persistent Homology of cosmic matter density field. https://doi.org/10.1142/s0219887825400067

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