Constructing realistic Szekeres models from initial and final data

• Main Author: Walters, Anthony Paul
• Other Authors: Hellaby, Charles
• Format: Dissertation
• Language: English
• Published: University of Cape Town 2015
• Subjects: Mathematics and Applied Mathematics
• Online Access: http://hdl.handle.net/11427/14382

The Szekeres family of inhomogeneous solutions, which are defined by six arbitrary metric functions, offers a wide range of possibilities for modelling cosmic structure. Within this family, the quasispherical case is the best understood, and is interpreted as being an arrangement on non-concentric mass shells, each a density dipole. 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 Lemaitre-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.