Growth of structure in the Szekeres class-II inhomogeneous cosmological models and the matter-dominated 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 large-scale 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 Friedmann-Lemaître-Robertson-Walker (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 non-linear perturbations. We integrate numerically the full exact growth rate equations for the flat and curved cases. We find that for the matter-dominated 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 non-linear perturbations. We also find that the Szekeres growth rate with an Einstein-de Sitter background is stronger than that of the well-known non-linear 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 matter-dominated era could suggest a substitute to the argument that dark matter is needed when using FLRW models to explain the enhanced growth and resulting large-scale structures that we observe today.PACS numbers: 98.80. Es,95.30.Sf

Relativistic numerical cosmology with silent universes

“…The code simsilun is publicly available via the Bitbucket repository * and is distributed under the terms of the GNU General Public License. The code can easily be modified to include further effects, such as light propagation (Räsänen, 2010;Bolejko, 2011;Clarkson et al, 2012;Bolejko & Ferreira, 2012;Troxel et al, 2014;Peel et al, 2014), modelling of inhomogeneous non-symmetrical cosmic structures (Bolejko, 2006(Bolejko, , 2007Ishak & Peel, 2012;Peel et al, 2012;Sussman & Delgado Gaspar, 2015;Sussman et al, 2016), and the impact of the local cosmological environment on astronomical observations (Bolejko et al, 2016).…”

Light propagation in Swiss-cheese models of random close-packed Szekeres structures: Effects of anisotropy and comparisons with perturbative results

“…This is unfortunate since real structures are not exactly spherically symmetric, making it important to know if spherical symmetry is essential for the agreement between Swiss cheese and perturbative results 2 . It is in this respect notable that anisotropic Szekeres models exhibit structure formation that deviates significantly from both that of the underlying LTB models and from predictions of perturbation theory [34][35][36][37][38]. In addition, it is very clear from figure 7a in [28] that light propagation is significantly affected by anisotropy; in that figure, it is seen that an initially radial light ray following an exact geodesic of an anisotropic Szekeres model moves through a significantly different density field than a light ray traced simply by using the Born approximation.…”

Differential cosmic expansion and the Hubble flow anisotropy

“…To our knowledge this paper contains the first ever study which seeks to use exact solutions of Einstein's equations to model structures giving rise to nonlinear expansion on scales comparable to those observed, constrained directly by both ray-tracing of the CMB and by the Hubble expansion field from actual surveys. While the Szekeres solution has been employed for a number of cosmological problems [56][57][58][59][60][61][62][63][64][65], we believe that this is also the first time that it has been used for ray-tracing simulations of local structures. We will see that although we are not able to match all features of the nonlinear Hubble expansion below the statistical homogeneity scale, with the Szekeres solution we can nonetheless match more features of the actual data than with other models, including the standard FLRW cosmology with a local boost of the Local Group of galaxies.…”