Related papers: Approximation Methods for Non-linear Gravitational…
Evolution of genus density is calculated from Gaussian initial conditions using Zel'dovich approximation. A new approach is introduced which formulates the desired quantity in a rotationally invariant manner. It is shown that normalized…
We investigate how observations of strong lensing can be used to infer cosmological parameters, in particular the equation of state of dark energy. We focus on the growth of the critical lines of lensing clusters with the source redshift as…
We investigate non-linear scaling relations for two-dimensional gravitational collapse in an expanding background using a 2D TreePM code and study the strongly non-linear regime ($\bar\xi \leq 200$) for power law models. Evolution of these…
We study the geometry and topology of the large-scale structure traced by galaxy clusters in numerical simulations of a box of side 320 $h^{-1}$ Mpc, and compare them with available data on real clusters. The simulations we use are…
I review recent progress in understanding and modeling galaxy clustering in cosmological simulations, with emphasis on models based on high-resolution dissipationless simulations. During the last decade, significant advances in our…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
These lectures cover various aspects of the statistical description of cosmological density fields. Observationally, this consists of the point process defined by galaxies, and the challenge is to relate this to the continuous density field…
We explore the morphological and dynamical evolution of galaxy clusters in simulations using scalar and vector-valued Minkowski valuations and the concept of fundamental plane relations. In this context, three questions are of fundamental…
We develop a systematic method to obtain the solution of the collisionless Boltzmann equation which describes the growth of large-scale structures as a perturbative series over the initial density perturbations. We give an explicit…
This paper presents an analytical formula that closely approximates the fully nonlinear power spectrum of matter fluctuations for redshift $z\approx 5$ to 0 over a wide range of cosmologically interesting flat models with varying matter…
An analytical understanding of the strongly nonlinear regime of gravitational collapse has been difficult to achieve. The only insight has been the stable clustering hypothesis, which assumes that the number of neighbors for objects…
We study the growth of large scale structure in two recently proposed non-standard cosmological models: the brane induced gravity model of Dvali, Gabadadze and Porrati (DGP) and the Cardassian models of Freese and Lewis. A general formalism…
The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are…
Among several analytic approximations for the growth of density fluctuations in the expanding Universe, Zel'dovich approximation in Lagrangian coordinate scheme is known to be unusually accurate even in mildly non-linear regime. This…
In hierarchical cosmologies the evolution of galaxy clustering depends both on cosmological quantities such as Omega and Lambda, which determine how dark matter halos form and evolve, and on the physical processes - cooling, star formation…
We generalize the spherical collapse model for the formation of bound objects to apply in a Universe with arbitrary positive cosmological constant. We calculate the critical condition for collapse of an overdense region and give exact…
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…
The notion of `adhesion' has been advanced for the phenomenon of stabilization of large-scale structure emerging from gravitational instability of a cold medium. Recently, the physical origin of adhesion has been identified: a systematic…
We present the clustering of galaxy clusters as a useful addition to the common set of cosmological observables. The clustering of clusters probes the large-scale structure of the Universe, extending galaxy clustering analysis to the…
In the standard picture of cosmological structure formation, initially random-phase fluctuations are amplified by non-linear gravitational instability to produce a final distribution of mass which is highly non-Gaussian and has…