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We show that the full dynamical freedom of the well known Szekeres models allows for the description of elaborated 3--dimensional networks of cold dark matter structures (over--densities and/or density voids) undergoing pancake collapse. By reducing Einsteins field equations to a set of evolution equations, which themselves reduce in the linear limit to evolution equations for linear perturbations, we determine the dynamics of such structures, with the spatial comoving location of each structure uniquely specified by standard early Universe initial conditions. By means of a representative example we examine in detail the density contrast, the Hubble flow and peculiar velocities of structures that evolved, from linear initial data at the last scattering surface, to fully non--linear 10--20 Mpc. scale configurations today. To motivate further research, we provide a qualitative discussion on the connection of Szekeres models with linear perturbations and the pancake collapse of the Zeldovich approximation. This type of structure modelling provides a coarse grained -- but fully relativistic non--linear and non--perturbative -- description of evolving large scale cosmic structures before their virialisation, and as such it has an enormous potential for applications in cosmological research.
We study the differences and equivalences between the non-perturbative description of the evolution of cosmic structure furnished by the Szekeres dust models (a non-spherical exact solution of Einsteins equations) and the dynamics of Cosmological Per
We examine the relation between the Szekeres models and relativistic Lagrangian perturbation schemes, in particular the Relativistic Zeldovich Approximation (RZA). We show that the second class of the Szekeres solutions is exactly contained within th
We consider the existence of an inflaton described by an homogeneous scalar field in the Szekeres cosmological metric. The gravitational field equations are reduced to two families of solutions which describe the homogeneous Kantowski-Sachs spacetime
The quasi-spherical Szekeres dust solutions are a generalization of the spherically symmetric Lemaitre-Tolman-Bondi dust models where the spherical shells of constant mass are non-concentric. The quasi-spherical Szekeres dust solutions can be conside
In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a high-dimensional dynamical system with multiple time scales. In this wo