Related papers: The Zeldovich approximation: key to understanding …
The large-scale structure of the Universe is characterised by a web-like structure made of voids, sheets, filaments, and knots. The structure of this so-called cosmic web is dictated by the local velocity shear tensor. In particular, the…
These lectures notes give an introduction to the fast developing area of research dealing with perturbative descriptions of the gravitational instability in an expanding universe. I just sketch the outlines of some proofs, and many…
A visualization of three-dimensional structures and cosmic flows is presented using information from the Extragalactic Distance Database V8k redshift catalog and peculiar velocities from the Cosmicflows-1 survey. Structures within a volume…
A lattice model for four dimensional Euclidean quantum general relativity is proposed for a simplicial spacetime. It is shown how this model can be expressed in terms of a sum over worldsheets of spin networks, and an interpretation of…
As an alternative way of describing the cosmological velocity field, we discuss the evolution of rotational invariants constructed from the velocity gradient tensor. Compared with the traditional divergence-vorticity decomposition, these…
The modeling of cosmological observables is based on the statistics of the matter density, velocity and gravitational fields in the Universe as a function of time. Typically, calculations are restricted to equal time correlations, where any…
We describe the Bayesian BARCODE formalism that has been designed towards the reconstruction of the Cosmic Web in a given volume on the basis of the sampled galaxy cluster distribution. Based on the realization that the massive compact…
A holistic view of the cosmological appearance and development of space is obtained by studying space as a spherically closed surface of a 4-sphere in a zero energy balance between motion and gravitation. Such an approach re-establishes…
The study of large-scale structure can benefit from accurate and robust identification of the cosmic web. Having such classification can facilitate a more complete extraction of cosmological information encoded therein. Classification…
We construct a geometric framework for cosmological large-scale structure based on optimal transport theory and Wasserstein geometry. In this framework, Ricci curvature on the probability measure space $\mathcal{P}_2(M)$ is characterized by…
The topology of large scale structure is studied as a function of galaxy type using the genus statistic. In hydrodynamical cosmological CDM simulations, galaxies form on caustic surfaces (Zeldovich pancakes) then slowly drain onto filaments…
It is possible to visualize the Cosmic Web as an interconnected network of one-dimensional filaments, two-dimensional sheets and three-dimensional volume-filling structures which we refer to as clusters. We have used the Local Dimension D,…
Structure formation in the Universe has been well-studied within the Eulerian and Lagrangian perturbation theories, where the latter performs substantially better in comparison with N-body simulations. Standing out is the celebrated…
This paper investigates evolution of cosmic structures in different environments. For this purpose the quasispherical Szekeres model is employed. The Szekeres model is an exact solution of the Einstein field equations within which it is…
We report the {\em first} systematic study of the supercluster-void network in the $\Lambda$CDM concordance cosmology treating voids and superclusters on an equal footing. We study the dark matter density field in real space smoothed with…
We introduce a multiscale topological description of the Megaparsec weblike cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of…
We analyze the structure and connectivity of the distinct morphologies that define the Cosmic Web. With the help of our Multiscale Morphology Filter (MMF), we dissect the matter distribution of a cosmological $\Lambda$CDM N-body computer…
Knowledge of the intrinsic shape of galaxy clusters is very important in investigating cosmic structure formation and astrophysical processes. The reconstruction of the 3-dimensional structure usually relies on deprojecting 2-dimensional…
We compare different nonlinear approximations to gravitational clustering in the weakly nonlinear regime, using as a comparative statistic the evolution of non-Gaussianity which can be characterised by a set of numbers $S_p$ describing…
The excursion set approach is a framework for estimating how the number density of nonlinear structures in the cosmic web depends on the expansion history of the universe and the nature of gravity. A key part of the approach is the…