[Paper Review] The cosmic web connection to the dark matter halo distribution through gravity

Francisco-Shu Kitaura, A. Balaguera-Antolínez+2 more|arXiv (Cornell University)|May 23, 2020

Galaxies: Formation, Evolution, Phenomena3 references4 citations

TL;DR

This paper proposes a novel framework linking the cosmic web to dark matter halo distributions using gravitational potential invariants, achieving unprecedented accuracy in reproducing halo clustering statistics. By leveraging tidal field and velocity shear tensor invariants within perturbation theory, it reproduces the power spectrum within 1% up to $k=0.72\,h\,{\rm Mpc}^{-1}$ and detects non-local bias at 4.8$\sigma$, proving that anisotropic clustering is essential for accurate field-level halo modeling in cosmological simulations and mock galaxy catalogs.

ABSTRACT

This work investigates the connection between the cosmic web and the halo distribution through the gravitational potential at the field level. We combine three fields of research, cosmic web classification, perturbation theory expansions of the halo bias, and halo (galaxy) mock catalogue making methods. In particular, we use the invariants of the tidal field and the velocity shear tensor as generating functions to reproduce the halo number counts of a reference catalogue from full gravity calculations, populating the dark matter field on a mesh well into the non-linear regime ($3\,h^{-1}\,{ m Mpc}$ scales). Our results show an unprecedented agreement with the reference power spectrum within 1% up to $k=0.72\,h\,{ m Mpc}^{-1}$. By analysing the three-point statistics on large scales (configurations of up to $k=0.2\,h\,{ m Mpc}^{-1}$), we find evidence for non-local bias at the 4.8 $σ$ confidence level, being compatible with the reference catalogue. In particular, we find that a detailed description of tidal anisotropic clustering on large scales is crucial to achieve this accuracy at the field level. These findings can be particularly important for the analysis of the next generation of galaxy surveys in mock galaxy production.

Motivation & Objective

• To establish a physically grounded, quantitative connection between the cosmic web and the distribution of dark matter halos using gravitational potential invariants.
• To improve the accuracy of halo mock catalogues by incorporating tidal anisotropy and non-local bias effects derived from the gravitational field.
• To test whether invariants of the tidal field and velocity shear tensor can reproduce large-scale clustering statistics—especially power spectrum and bi-spectrum—of reference $N$-body simulations.
• To assess the necessity of including higher-order anisotropic bias terms for accurate field-level halo distribution modeling in cosmological surveys.
• To provide a foundation for next-generation galaxy surveys by enabling more accurate, physically motivated mock galaxy production with reduced systematics.

Proposed method

• Uses invariants of the tidal field tensor and velocity shear tensor as generating functions to model halo number counts at the field level.
• Applies perturbation theory expansions of halo bias to describe non-local and non-linear dependencies of halos on the gravitational potential.
• Employs full gravity simulations on a mesh down to $3\,h^{-1}\,{\rm Mpc}$ scales to compute the gravitational potential and its invariants.
• Constructs halo mock catalogues using the invariants as biasing functions, calibrated against a reference $N$-body simulation.
• Performs power spectrum and bi-spectrum analysis to validate the model against the reference catalogue across scales up to $k=0.72\,h\,{\rm Mpc}^{-1}$.
• Uses a Markov Chain Monte Carlo rejection algorithm to learn optimal bias kernel parameters from the reference simulation, minimizing uncertainties.

Experimental results

Research questions

• RQ1 Can the invariants of the tidal field and velocity shear tensor accurately reproduce the halo power spectrum up to $k=0.72\,h\,{\rm Mpc}^{-1}$?
• RQ2 To what extent does including anisotropic clustering terms improve the accuracy of halo distribution modeling compared to isotropic or local bias models?
• RQ3 Is non-local bias detectable at high significance in the three-point statistics, and does it align with the reference simulation?
• RQ4 How do the invariants of the gravitational potential relate to cosmic web morphology and halo clustering across different web types?
• RQ5 Can this framework be extended to improve covariance matrix estimation and galaxy mock production for upcoming cosmological surveys?

Key findings

• The model reproduces the reference halo power spectrum within 1% accuracy up to $k=0.72\,h\,{\rm Mpc}^{-1}$, demonstrating exceptional agreement with the $N$-body simulation.
• Non-local bias is detected at the 4.8$\sigma$ confidence level in the three-point statistics, confirming its importance for accurate clustering modeling.
• Incorporating the invariants of the tidal shear tensor significantly improves accuracy on large scales, validating the necessity of anisotropic bias descriptions.
• The bi-spectrum analysis shows that invariants become essential already at $k_1 = k_2 = 0.05\,h\,{\rm Mpc}^{-1}$, indicating early relevance of anisotropic clustering.
• The framework enables a consistent, physically motivated description of halo bias using only a few terms derived from gravitational field invariants.
• The results suggest that future galaxy mock catalogs based on these invariants could achieve high accuracy in two-, three-, and four-point statistics, reducing systematics in cosmological inference.