Coarse-grained description of cosmic structure from Szekeres models

TL;DR

This paper demonstrates how Szekeres models can describe complex 3D cosmic structures evolving from linear initial conditions to non-linear scales, offering a fully relativistic, non-perturbative approach to large-scale structure formation.

Contribution

It introduces a method to model detailed 3D cosmic structures using Szekeres models, bridging linear perturbations and non-linear evolution in a relativistic framework.

Findings

Successfully modeled 10-20 Mpc structures from linear initial data

Analyzed density contrast, Hubble flow, and velocities of evolved structures

Connected Szekeres models with linear perturbation theory and pancake collapse

Abstract

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 Einstein's 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.