Related papers: Using the Zeldovich dynamics to test expansion sch…
We describe various expansion schemes that can be used to study gravitational clustering. Obtained from the equations of motion or their path-integral formulation, they provide several perturbative expansions that are organized in different…
We investigate the properties of the standard perturbative expansions which describe the early stages of the dynamics of gravitational clustering. We show that for hierarchical scenarios with no small-scale cutoff perturbation theory always…
We discuss various analytical approximation methods for following the evolution of cosmological density perturbations into the strong (i.e. nonlinear) clustering regime. These methods can be classified into five types: (i) simple…
Nonlinear approximation methods such as the Zeldovich approximation, and more recently the frozen flow and linear potential approximations, are sometimes used to simulate nonlinear gravitational instability in the expanding Universe. We…
We develop a path-integral formalism to study the formation of large-scale structures in the universe. Starting from the equations of motion of hydrodynamics (single-stream approximation) we derive the action which describes the statistical…
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…
I report on controlled comparison of gravitational approximation schemes linear/lognormal/adhesion/frozen-flow/Zel'dovich(ZA) and ZA's second--order generalization. In the last two cases we also created new versions of the approximation by…
Among various analytic approximations for the growth of density fluctuations in the expanding Universe, Zel'dovich approximation and its extensions in Lagrangian scheme are known to be accurate even in mildly non-linear regime. The aim of…
In an expanding universe, velocity field and gravitational force field are proportional to each other in the linear regime. Neither of these quantities evolve in time and these can be scaled suitably so that the constant of proportionality…
A new exact nonlinear Newtonian solution for a plane matter flow superimposed on the isotropic Hubble expansion is reported. The dynamical effect of cosmic vacuum is taken into account. The solution describes the evolution of nonlinear…
We have recently learned that the Zeldovich approximation can be successfully used for a far wider range of gravitational instability scenarios than formerly proposed; we study here how to extend this range. In previous work we studied the…
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…
The Zeldovich approximation, 1st order Lagrangian perturbation theory, provides a good description of the clustering of matter and galaxies on large scales. The acoustic feature in the large-scale correlation function of galaxies imprinted…
We investigate the weakly non-linear evolution of cosmic gravitational clustering in phase space by looking at the Zel'dovich solution in the discrete wavelet transform (DWT) representation. We show that if the initial perturbations are…
We study the development of gravitational instability in the strongly non-linear regime. For this purpose we use a number of statistical indicators such as filamentary statistics, spectrum of overdense/underdense regions and the void…
Non-linear gravitational collapse introduces non-Gaussian statistics into the matter fields of the late Universe. As the large-scale structure is the target of current and future observational campaigns, one would ideally like to have the…
This work outlines an exact combinatorial approach to finite coagulating systems through recursive equations and use of generating function method. In the classic approach the mean-field Smoluchowski coagulation is used. However, the…
During the evolution of density inhomogeneties in an $\Omega=1$, matter dominated universe, the typical density contrast changes from $\delta\simeq 10^{-4}$ to $\delta\simeq 10^2$. However, during the same time, the typical value of the…
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…
We have considered linear two point correlations of the form $1/{x^{\gamma}}$ which are known to have a self-similar behaviour in a $\Omega=1$ universe. We investigate under what conditions the non-linear corrections, calculated using the…