Large-scale growth evolution in the Szekeres inhomogeneous cosmological models with comparison to growth data

Abstract

We use the Szekeres inhomogeneous cosmological models to study the growth of large-scale structure in the universe including nonzero spatial curvature and a cosmological constant. In particular, we use the Goode and Wainwright formulation of the solution, as in this form the models can be considered to represent exact nonlinear perturbations of an averaged background. We identify a density contrast in both classes I and II of the models, for which we derive growth evolution equations. By including $\ensuremath{\Lambda}$, the time evolution of the density contrast as well as kinematic quantities of interest can be tracked through the matter- and $\ensuremath{\Lambda}$-dominated cosmic eras up to the present and into the future. In class I, we consider a localized cosmic structure representing an overdensity neighboring a central void, surrounded by an almost Friedmann-Lema\^{\i}tre-Robertson-Walker background, while for class II, the exact perturbations exist globally. In various models of class I and class II, the growth rate is found to be stronger in the matter-dominated era than that of the standard lambda-cold dark matter ($\ensuremath{\Lambda}\mathrm{CDM}$) cosmology, and it is suppressed at later times due to the presence of the cosmological constant. We find that there are Szekeres models able to provide a growth history similar to that of $\ensuremath{\Lambda}\mathrm{CDM}$ while requiring less matter content and nonzero spatial curvature, which speaks to the importance of including the effects of large-scale inhomogeneities in analyzing the growth of large-scale structure. Using data for the growth factor $f$ from redshift space distortions and the Lyman-$\ensuremath{\alpha}$ forest, we obtain best fit parameters for class II models and compare their ability to match observations with $\ensuremath{\Lambda}\mathrm{CDM}$. We find that there is negligible difference between best fit Szekeres models with no priors and those for $\ensuremath{\Lambda}\mathrm{CDM}$, both including and excluding Lyman-$\ensuremath{\alpha}$ data. We also find that the standard growth index $\ensuremath{\gamma}$ parametrization cannot be applied in a simple way to the growth in Szekeres models, so a direct comparison of the function $f$ to the data is performed. We conclude that the Szekeres models can provide an exact framework for the analysis of large-scale growth data that includes inhomogeneities and allows for different interpretations of observations.