Growth of Structure in the Szekeres Inhomogeneous Cosmological Models

Mathematics – Logic

Scientific paper

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Scientific paper

We investigate the effect of incorporating inhomogeneities into cosmological models. We focus on the growth of large-scale structure in the class II Szekeres models to see how it compares to that of the linearly perturbed Friedmann-Lemaître-Roberston-Walker (FLRW) solution. The Szekeres models are exact solutions to the Einstein field equations with no symmetries and an irrotational dust source. We use the formulation introduced by Goode and Wainwright, who considered the solutions as exact non-linear perturbations around a smooth FLRW background. In this form, the solutions are therefore well-suited for studying the growth of large-scale structure. Using the Raychaudhuri equation, we derive an exact equation for the growth rate that exhibits a linear part identical to the perturbed FLRW result plus additional non-linear terms. We integrate the equation numerically and examine the growth behavior in flat and curved universes that include a cosmological constant. We find that a flat Szekeres model with fractional density parameters equal to the accepted Lambda-Cold Dark Matter (ΛCDM) values experiences significantly stronger growth than its ΛCDM counterpart. Further, we are finding that a Szekeres model with only 4% baryonic matter and a cosmological constant can mimic the growth history of ΛCDM and remain consistent with observations. This work is supported in part by a grant from NASA.

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