Caustic Skeleton & Cosmic Web

Abstract

We present a general formalism for identifying the caustic structure of an evolving mass distribution in an arbitrary dimensional space. For the class of Hamiltonian fluids the identification corresponds to the classification of singularities in Lagrangian catastrophe theory. Based on this we develop a theoretical framework for the formation of the cosmic web, and specifically those aspects that characterize its unique nature: its complex topological connectivity and multiscale spinal structure of sheetlike membranes, elongated filaments and compact cluster nodes. The present work represents an extension of the work by Arnol'd et al., who classified the caustics for the 1- and 2-dimensional Zel'dovich approximation. His seminal work established the role of emerging singularities in the formation of nonlinear structures in the universe. At the transition from the linear to nonlinear structure evolution, the first complex features emerge at locations where different fluid elements cross to establish multistream regions. The classification and characterization of these mass element foldings can be encapsulated in caustic conditions on the eigenvalue and eigenvector fields of the deformation tensor field. We introduce an alternative and transparent proof for Lagrangian catastrophe theory, and derive the caustic conditions for general Lagrangian fluids, with arbitrary dynamics, including dissipative terms and vorticity. The new proof allows us to describe the full 3-dimensional complexity of the gravitationally evolving cosmic matter field. One of our key findings is the significance of the eigenvector field of the deformation field for outlining the spatial structure of the caustic skeleton. We consider the caustic conditions for the 3-dimensional Zel'dovich approximation, extending earlier work on those for 1- and 2-dimensional fluids towards the full spatial richness of the cosmic web.

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Cited by in corpus (30)

• Baryons in the CosmicWeb of IllustrisTNG - I: Gas in Knots, Filaments, Sheets and Voids
• Populations of filaments from the distribution of galaxies in numerical simulations
• Phase-space structure of protohalos: Vlasov versus Particle-Mesh
• Lagrangian cosmological perturbation theory at shell-crossing
• Large-Scale Velocity Dispersion and the Cosmic Web
• Semiclassical path to cosmic large-scale structure
• Intergalactic filaments spin
• Cosmological Vlasov-Poisson equations for dark matter: Recent developments and connections to selected plasma problems
• Beta-Skeleton Analysis of the Cosmic Web
• Quantum caustics and the hierarchy of light cones in quenched spin chains
• Caustics in quantum many-body dynamics
• The cosmic web connection to the dark matter halo distribution through gravity
• Violent relaxation in quantum fluids with long-range interactions
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• Cold dark matter protohalo structure around collapse: Lagrangian cosmological perturbation theory versus Vlasov simulations
• On the origin of cosmic web
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• Improving SDSS cosmological constraints through $\beta$-skeleton weighted correlation functions
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• Active Caustics
• Post-collapse Lagrangian perturbation theory in three dimensions
• Enhancing Cosmological Constraints by Two-dimensional $\beta$-cosmic-web Weighted Angular Correlation Functions