Related papers: Local Approximations to the Gravitational Collapse…
This paper reviews the essential physics of gravitational instability in a Robertson-Walker background spacetime. Three approaches are presented in a pedagogical manner, based on (1) the Eulerian fluid equations, (2) the Lagrangian…
We solve the nonlinear evolution of pressureless, irrotational density fluctuations in a perturbed Robertson-Walker spacetime using a new Lagrangian method based on the velocity gradient and gravity gradient tensors. Borrowing results from…
Few recent generations of cosmologists have solved non-local newtonian equations of the gravitational instability in an expanding universe. In this approach pancaking is the predominant form of first collapsing objects. Relativistic…
Non-spherical dynamical approximations and models for the gravitational collapse are used to extend the well-known Press \& Schechter (PS) approach, in order to determine analytical expressions for the mass function of cosmic structures.…
We investigate the accuracy of the frozen--flow approximation (FFA), recently proposed by Matarrese \etal (1992), for following the nonlinear evolution of cosmological density fluctuations under gravitational instability. We compare a…
An analytic approximation to the mass function for gravitationally bound objects is presented. We base on the Zel'dovich approximation to extend the Press-Schechter formalism to a nonspherical dynamical model. A simple extrapolation of that…
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…
Two quasi-linear approximations, the frozen flow approximation (FFA) and the frozen potential approximation (FPA), have been proposed recently for studying the evolution of a collisionless self-gravitating fluid. In the FFA it is assumed…
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…
In this paper we review a recently developed approximate method for investigation of dynamics of compressible ellipsoidal figures. Collapse and subsequent behaviour are described by a system of ordinary differential equations for time…
We compare relativistic approximation methods, which describe gravitational instability in the expanding universe, in a spherically symmetric model. Linear perturbation theory, second-order perturbation theory, relativistic Zel'dovich…
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…
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…
Why does the Zel'dovich approximation (ZA) work well to describe gravitational collapse in the universe? This problem is examined by focusing on its dependence on the dimensionality of the collapse. The ZA is known to be exact for a…
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…
Since the early seventies, there was a conjecture that the first collapse of a selfgravitating dust--like medium (appropriate approximation for nonbaryonic dark matter) results in the formation of a ``pancake" object, that is a thin…
We present a comparative analysis of several methods, known as local Lagrangian approximations, which are aimed to the description of the nonlinear evolution of large-scale structure. We have investigated various aspects of these…
We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasilinear scales. The Lagrangian theory of gravitational instability of an Einstein-de…
We study gravitational collapse of a spherical fluid in nonrelativistic general covariant theory of the Ho\v{r}ava-Lifshitz gravity with the projectability condition and an arbitrary coupling constant $\lambda$, where $|\lambda - 1|$…
Some recently proposed approximations to follow the non--linear evolution of collisionless matter perturbations in the universe are reviewed. The first one, called frozen--flow approximation, is an Eulerian method within Newtonian theory,…