Cosmic Web & Caustic Skeleton: non-linear Constrained Realizations -- 2D case studies

Job Feldbrugge; Rien van de Weygaert

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Cosmic Web & Caustic Skeleton: non-linear Constrained Realizations -- 2D case studies

Job Feldbrugge, Rien van de Weygaert

Cosmology and Nongalactic Astrophysics · Submitted 15 Dec 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Applied to cosmological N-body simulations, the proposed techniques pave the way towards a systematic investigation of the evolution of the progenitors of the present-day walls, filaments, and clusters, and the embedded galaxies, putting flesh on the bones of the caustic skeleton.

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arXiv ID2212.07840 (version 1)

Pith IDYNTSPBPB, Pith's permanent record of this paper and its review

CitationJob Feldbrugge, Rien van de Weygaert. "Cosmic Web & Caustic Skeleton: non-linear Constrained Realizations -- 2D case studies." arXiv:2212.07840 (2022). https://pith.science/paper/YNTSPBPB

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What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.72 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.03 · states quantitative result 0.04 · compares with prior results 0.10 · mentions code or data availability 0.03.

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The cosmic web consists of a complex configuration of voids, walls, filaments, and clusters, which formed under the gravitational collapse of Gaussian fluctuations. Understanding under what conditions these different structures emerge from simple initial conditions, and how different cosmological models influence their evolution, is central to the study of the large-scale structure. Here, we present a general formalism for setting up initial random density and velocity fields satisfying non-linear constraints for specialized N-body simulations. These allow us to link the non-linear conditions on the eigenvalue and eigenvector fields of the deformation tensor, as specified by caustic skeleton theory, to the current-day cosmic web. By extending constrained Gaussian random field theory, and the corresponding Hoffman-Ribak algorithm, to non-linear constraints, we probe the statistical properties of the progenitors of the walls, filaments, and clusters of the cosmic web. Applied to cosmological N-body simulations, the proposed techniques pave the way towards a systematic investigation of the evolution of the progenitors of the present-day walls, filaments, and clusters, and the embedded galaxies, putting flesh on the bones of the caustic skeleton. The developed nonlinear constrained random field theory is valid for generic cosmological conditions. For ease of visualization, the case study presented here probes the two-dimensional caustic skeleton.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The cosmic web consists of a complex configuration of voids, walls, filaments, and clusters, which formed under the gravitational collapse of Gaussian fluctuations.	background 1.00	0.05	0.03	asserted 1.00
s1	Understanding under what conditions these different structures emerge from simple initial conditions, and how different cosmological models influence their evolution, is central to the study of the large-scale structure.	background 0.97	0.04	0.03	asserted 1.00
s2	Here, we present a general formalism for setting up initial random density and velocity fields satisfying non-linear constraints for specialized N-body simulations.	contribution 0.81	0.94	0.09	asserted 1.00
s3	These allow us to link the non-linear conditions on the eigenvalue and eigenvector fields of the deformation tensor, as specified by caustic skeleton theory, to the current-day cosmic web.	method 0.53	0.71	0.14	asserted 0.97
s4	By extending constrained Gaussian random field theory, and the corresponding Hoffman-Ribak algorithm, to non-linear constraints, we probe the statistical properties of the progenitors of the walls, filaments, and clusters of the cosmic web.	method 0.77	0.89	0.15	asserted 0.93
s5	Applied to cosmological N-body simulations, the proposed techniques pave the way towards a systematic investigation of the evolution of the progenitors of the present-day walls, filaments, and clusters, and the embedded galaxies, putting flesh on the bones of the caustic skeleton.	future work 0.66	0.50	0.42	hedged possibility 0.59
s6	The developed nonlinear constrained random field theory is valid for generic cosmological conditions.	contribution 0.48	0.75	0.12	asserted 1.00
s7	For ease of visualization, the case study presented here probes the two-dimensional caustic skeleton.	limitation 0.76	0.77	0.03	asserted 0.96

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.74.

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The paper

Original abstract

The cosmic web consists of a complex configuration of voids, walls, filaments, and clusters, which formed under the gravitational collapse of Gaussian fluctuations. Understanding under what conditions these different structures emerge from simple initial conditions, and how different cosmological models influence their evolution, is central to the study of the large-scale structure. Here, we present a general formalism for setting up initial random density and velocity fields satisfying non-linear constraints for specialized N-body simulations. These allow us to link the non-linear conditions on the eigenvalue and eigenvector fields of the deformation tensor, as specified by caustic skeleton theory, to the current-day cosmic web. By extending constrained Gaussian random field theory, and the corresponding Hoffman-Ribak algorithm, to non-linear constraints, we probe the statistical properties of the progenitors of the walls, filaments, and clusters of the cosmic web. Applied to cosmological N-body simulations, the proposed techniques pave the way towards a systematic investigation of the evolution of the progenitors of the present-day walls, filaments, and clusters, and the embedded galaxies, putting flesh on the bones of the caustic skeleton. The developed nonlinear constrained random field theory is valid for generic cosmological conditions. For ease of visualization, the case study presented here probes the two-dimensional caustic skeleton.

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3 arXiv papers cite this in 8 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 4 sentences without a confident label

Cites it as support 1 paper

Indeed, this is exactly what the caustic skeleton theory of cosmic web formation stipulates [ref] : it establishes the central role of deformation eigenvalues and eigenvectors in the emergence of the structural pattern of the cosmic web, and hence how the primordial non-Gaussianities of these fields carry over into the non-Gaussian nature of the present-day cosmic web.

Statistics of tidal and deformation eigenvalue fields in the primordial Gaussian matter distribution: the two-dimensional case · Eigenvalue Fields & Primordial Cosmic Web: illustration · 0.96

Cites it as background 1 paper

Additionally, the DM distribution in filaments has been characterized using theoretical frameworks for the dynamics of the formation of the cosmic web [ref] .

Dark matter decay signals in cosmic filaments · Introduction · 0.98

What it cites · 92 sentences without a confident label

Builds on 3 papers

Given the importance of basing the analysis of cosmic web observations on a good analytical model for its non-linear evolution, the present study involves the further development of the Caustic Skeleton model of the cosmic web that we introduced in [ref] .

Caustic Skeleton & Cosmic Web · The cosmic web · 0.97
It is an extension and elaboration of the linear constrained field formalism introduced by [ref] , and further developed in [ref] and [ref] .

Constraining Peaks in Gaussian Primordial Density Fields: an Application of the Hoffman-Ribak Method · Introduction · 0.98
In this study, we extend and elaborate our analytical model for the formation of the cosmic web [ref] , and its complex multiscale network of filaments and sheets, by the Caustic Skeleton model [ref] .

How Filaments are Woven into the Cosmic Web · Introduction · 0.91

Uses the method or tool of 3 papers

The caustic conditions [ref] allow us to infer exactly the location of the singularities in the matter distribution, the caustics.

Caustic Skeleton & Cosmic Web · Multistream regions and caustic skeleton · 0.87
To this end, we may use the Hoffman-Ribak method [ref] to generate Gaussian realizations obeying the constraint values $c$.

Constraining Peaks in Gaussian Primordial Density Fields: an Application of the Hoffman-Ribak Method · Non-linear constrained random fields: formalism · 1.00
To systematically study these initial conditions we use constrained Gaussian random field theory [ref] .

Constrained realizations and minimum variance reconstruction of non-Gaussian random fields · Linear constraints: constrained Gaussian random fields · 0.99

Compares with 1 paper

This should be compared to the splice method [ref] which relies on a large number of linear constraints.

The causal effect of environment on halo mass and concentration · Conclusion · 0.99

Cites as support 3 papers

The explicit demonstration by [ref] revealed their importance in outlining the weblike structure.

Caustic Skeleton & Cosmic Web · Primordial deformation field and cosmic web · 0.99
This is in line with the expectation for the constrained mass distribution around protofilaments, as has been pointed out by the study of [ref] .

Constraining Peaks in Gaussian Primordial Density Fields: an Application of the Hoffman-Ribak Method · Cusp mean field · 0.98
Recently, some numerical evidence on different filament classes has been found [ref] .

Populations of filaments from the distribution of galaxies in numerical simulations · Conclusion · 0.99

Cites as background 7 papers

Caustic skeleton theory provides a set of conditions for the emergence of various caustics classified by Lagrangian catastrophe theory in fluids dynamics [ref] .

Caustic Skeleton & Cosmic Web · Conclusion · 0.95
Caustic skeleton theory provides a set of conditions for the emergence of various caustics classified by Lagrangian catastrophe theory in fluids dynamics [ref] .

The Zeldovich approximation: key to understanding Cosmic Web complexity · Conclusion · 0.95
Well-known in this context are the CLUES simulations [ref] .

Cosmicflows Constrained Local UniversE Simulations · Caustic skeleton & non-linear constraints · 0.94

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