Related papers: Testing Higher--Order Lagrangian Perturbation Theo…
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…
Approximations to the exact solutions for gravitational instability in the expanding Universe are extremely useful for understanding the evolution of large--scale structure. We report on a series of tests of Newtonian Lagrangian…
Fundamental assumptions which form the basis of models for large-scale structure in the Universe are sketched in light of a Lagrangian description of inhomogeneities. This description is introduced for Newtonian self-gravitating flows. On…
We report on a series of tests of Newtonian Lagrangian perturbation schemes using N--body simulations for various power--spectra with scale--independent indices in the range $-3$ to $+1$. The models have been evolved deeply into the…
The Lagrangian theory of gravitational instability of homogeneous-isotropic Friedman-Lemaitre cosmogonies investigated and solved in the series of papers by Buchert (1989), (1992), Buchert & Ehlers (1993), Buchert (1993a,b), Ehlers &…
The Lagrangian perturbation theory on Friedman-Lemaitre cosmologies investigated and solved up to the second order in earlier papers (Buchert 1992, Buchert \& Ehlers 1993) is evaluated up to the third order. On its basis a model for…
The Eulerian and Lagrangian second-order perturbation theories are solved explicitly in closed forms in $\Omega \neq 1$ and $\Lambda \neq 0$ {}Friedmann-Lema\^{\i}tre models. I explicitly write the second-order theories in terms of closed…
This paper deals with the time evolution in the matter era of perturbations in Friedman-Lemaitre models with arbitrary density parameter $\Omega$, with either a zero cosmological constant, $\Lambda = 0$, or with a non-zero cosmological…
We investigate the performance of Lagrangian perturbation theory up to the second order for two scenarios of cosmological large-scale structure formation, SCDM (standard cold dark matter) and BSI (broken scale invariance). The latter model…
We report on the performance of Lagrangian perturbation theory up to the second order for the standard cold dark matter (SCDM) and broken scale invariance (BSI) scenarios. We normalize both models to the COBE data, the BSI model serves as…
The Lagrangian perturbation theory on Friedmann-Lemaitre cosmologies is compared with numerical simulations (tree-, adaptive P$^3$M- and PM codes). In previous work we have probed the large-scale performance of the Lagrangian perturbation…
We investigate the Lagrangian perturbation theory of a general dark energy models with a constant equation of state, \omega, and derive the fitting form of the fastest growing mode solutions up to the third order. These fitting forms are…
We present high--spatial resolution studies of the density field as predicted by Lagrangian perturbation approximations up to the third order. The first--order approximation is equivalent to the ``Zel'dovich approximation'' for the type of…
Previous work in the literature has studied the Hamiltonian structure of an R-squared model of gravity with torsion in a closed Friedmann-Robertson-Walker universe. Within the framework of Dirac's theory, torsion is found to lead to a…
The behavior of the second-order Lagrangian structure functions on state-of-the-art numerical data both in two and three dimensions is studied. On the basis of a phenomenological connection between Eulerian space-fluctuations and the…
We present a simple and intuitive approximation for solving perturbation theory (PT) of small cosmic fluctuations. We consider only the spherically symmetric or monopole contribution to the PT integrals, which yields the exact result for…
We extensively develop a perturbation theory for nonlinear cosmological dynamics, based on the Lagrangian description of hydrodynamics. We solve hydrodynamic equations for a self-gravitating fluid with pressure, given by a polytropic…
Many recent studies have highlighted certain failures of the standard Eulerian-space cosmological perturbation theory (SPT). Its problems include (1) not capturing large-scale bulk flows [leading to an O(1) error in the 1-loop SPT…
The projectability of Poincar\'e-Cartan forms in a third-order jet bundle $J^3\pi$ onto a lower-order jet bundle is a consequence of the degenerate character of the corresponding Lagrangian. This fact is analyzed using the constraint…
Lagrangian perturbation theory for cosmological fluid describes structure formation in the quasi-nonlinear stage well. In a previous paper, we presented a third-order perturbative equation for Lagrangian perturbation with pressure. There we…