Constructing Realistic Szekeres Models from Initial and Final Data

TL;DR

This paper presents a method to construct realistic Szekeres inhomogeneous cosmological models from initial and final data, deriving explicit formulas for model functions and demonstrating the approach with MATLAB simulations.

Contribution

It introduces a novel procedure to build Szekeres models using boundary data, explicitly deriving functions based on density and dipole orientation, and implements it computationally.

Findings

Explicit analytic expressions for Szekeres functions derived.

Successful MATLAB implementation and simulation of model evolution.

Enhanced ability to model cosmic structures with realistic inhomogeneities.

Abstract

The Szekeres family of inhomogeneous solutions, which are defined by six arbitrary metric functions, offers a wide range of possibilities for modelling cosmic structure. Here we present a model construction procedure for the quasispherical case using given data at initial and final times. Of the six arbitrary metric functions, the three which are common to both Szekeres and Lema\^itre-Tolman models are determined by the model construction procedure of Krasinski & Hellaby. For the remaining three functions, which are unique to Szekeres models, we derive exact analytic expressions in terms of more physically intuitive quantities - density profiles and dipole orientation angles. Using MATLAB, we implement the model construction procedure and simulate the time evolution.