Growth of structure in the Szekeres classII inhomogeneous cosmological models and the matterdominated era
Abstract
This study belongs to a series devoted to using the Szekeres inhomogeneous models in order to develop a theoretical framework where cosmological observations can be investigated with a wider range of possible interpretations. While our previous work addressed the question of cosmological distances versus redshift in these models, the current study is a start at looking into the growth rate of largescale structure. The Szekeres models are exact solutions to Einstein’s equations that were originally derived with no symmetries. We use here a formulation of the Szekeres models that is due to Goode and Wainwright, who considered the models as exact perturbations of a FriedmannLemaîtreRobertsonWalker (FLRW) background. Using the Raychaudhuri equation we write, for the two classes of the models, exact growth equations in terms of the under/overdensity and measurable cosmological parameters. The new equations in the overdensity split into two informative parts. The first part, while exact, is identical to the growth equation in the usual linearly perturbed FLRW models, while the second part constitutes exact nonlinear perturbations. We integrate numerically the full exact growth rate equations for the flat and curved cases. We find that for the matterdominated cosmic era, the Szekeres growth rate is up to a factor of three to five stronger than the usual linearly perturbed FLRW cases, reflecting the effect of exact Szekeres nonlinear perturbations. We also find that the Szekeres growth rate with an Einsteinde Sitter background is stronger than that of the wellknown nonlinear spherical collapse model, and the difference between the two increases with time. This highlights the distinction when we use general inhomogeneous models where shear and a tidal gravitational field are present and contribute to the gravitational clustering. Additionally, it is worth observing that the enhancement of the growth found in the Szekeres models during the matterdominated era could suggest a substitute to the argument that dark matter is needed when using FLRW models to explain the enhanced growth and resulting largescale structures that we observe today.
 Publication:

Physical Review D
 Pub Date:
 April 2012
 DOI:
 10.1103/PhysRevD.85.083502
 arXiv:
 arXiv:1104.2590
 Bibcode:
 2012PhRvD..85h3502I
 Keywords:

 98.80.Jk;
 95.30.Sf;
 98.80.Es;
 Mathematical and relativistic aspects of cosmology;
 Relativity and gravitation;
 Observational cosmology;
 Astrophysics  Cosmology and Extragalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 18 pages, 4 figures, matches PRD accepted version