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Cold dark matter (CDM) can be thought of as a 2D (or 3D) sheet of particles in 4D (or 6D) phase-space due to its negligible velocity dispersion. The large-scale structure, also called the cosmic web, is thus a result of the topology of the…
The local theory of the critical lines of 2D and 3D Gaussian fields that underline the cosmic structures is presented. In the context of cosmological matter distribution the subset of critical lines of the 3D density field serves to…
The large scale structure of the universe is a complex web of clusters, filaments, and voids. Its properties are informed by galaxy redshift surveys and measurements of peculiar velocities. Wiener Filter reconstructions recover…
In these lecture notes I review the theory of the non--linear evolution of cosmological perturbations in a self--gravitating collisionless medium, with vanishing vorticity. The problem is first analyzed in the context of the Newtonian…
We present, for the first time, a Local Universe (LU) characterization using high precision constrained $N$-body simulations based on self-consistent phase-space reconstructions of the large-scale structure in the Two-Micron All-Sky Galaxy…
A short overview is given on the development of our present paradigm of the large scale structure of the Universe with emphasis on the role of Ya. B. Zeldovich. Next we use the Sloan Digital Sky Survey data and show that the distribution of…
We discuss the intimate relationship between the filamentary features and the rare dense compact cluster nodes in this network, via the large scale tidal field going along with them, following the cosmic web theory developed Bond et al. The…
Gravitational-collapse-based explanations of the cosmic web lead to problems in estimating the total mass in the universe. A first-principles several-scales model is developed here for the structural organisation of cosmic matter in a flat…
We review the analysis of the Cosmic Web by means of an extensive toolset based on the use of Delaunay and Voronoi tessellations. The Cosmic Web is the salient and pervasive foamlike pattern in which matter has organized itself on scales of…
A fundamental hypothesis for the interpretation of the measured large-scale line-of-sight peculiar velocities of galaxies is that the large-scale cosmic flows are irrotational. In order to assess the validity of this assumption, we…
Cosmic filaments are the main transport channels of matter in the Megaparsec universe, and represent the most prominent structural feature in the matter and galaxy distribution. Here we describe and define the physical and dynamical nature…
Understanding the structure of the matter distribution in the Universe due to the action of the gravitational instability -- the cosmic web -- is complicated by lack of direct analytic access to the nonlinear domain of structure formation.…
The geometry of the cosmic web drives in part the spin acquisition of galaxies. This can be explained in a Lagrangian framework, by identifying the specific long-wavelength correlations within the primordial Gaussian random field which are…
The emergence of cosmic structure is commonly considered one of the most complex phenomena in Nature. However, this complexity has never been defined nor measured in a quantitative and objective way. In this work we propose a method to…
In this paper we explore the use of spatial clustering algorithms as a new computational approach for modeling the cosmic web. We demonstrate that such algorithms are efficient in terms of computing time needed. We explore three distinct…
The growth of large-scale cosmic structure is a beautiful exemplification of how complexity can emerge in our Universe, starting from simple initial conditions and simple physical laws. Using {\enzo} cosmological numerical simulations, I…
The phase space distribution of matter out to $\sim 100 \rm Mpc$ is probed by two types of observational data: galaxy redshift surveys and peculiar motions of galaxies. Important information on the process of structure formation and…
Studying the structures (halos and galaxies) within the cosmic environments (void, sheet, filament, and node) where they reside is an ongoing attempt in cosmological studies. The link between the properties of structures and the cosmic…
The cosmic web consists of a nested hierarchy of structures: voids, walls, filaments, and clusters. These structures interconnect and can encompass one another, collectively shaping an intricate network. Here we introduce the Hierarchical…
The network of filaments with embedded clusters surrounding voids seen in maps derived from redshift surveys and reproduced in simulations has been referred to as the cosmic web. A complementary description is provided by considering the…