Exact nonlinear inhomogeneities in $\Lambda$CDM cosmology

Abstract

At a time when galaxy surveys and other observations are reaching unprecedented sky coverage and precision it seems timely to investigate the effects of general relativistic nonlinear dynamics on the growth of structures and on observations. Analytic inhomogeneous cosmological models are an indispensable way of investigating and understanding these effects in a simplified context. In this paper, we develop exact inhomogeneous solutions of general relativity with pressureless matter (dust, describing cold dark matter) and cosmological constant $\Lambda$, which can be used to model an arbitrary initial matter distribution along one line of sight. In particular, we consider the second class Szekeres models with $\Lambda$ and split their dynamics into a flat $\Lambda$CDM background and exact nonlinear inhomogeneities, obtaining several new results. One single metric function $Z$ describes the deviation from the background. We show that $F$, the time dependent part of $Z$, satisfies the familiar linear differential equation for $\delta$, the first-order density perturbation of dust, with the usual growing and decaying modes. In the limit of small perturbations, $\delta \approx F$ as expected, and the growth of inhomogeneities links up exactly with standard perturbation theory. We provide analytic expressions for the exact nonlinear $\delta$ and the growth factor in our models. For the case of over-densities, we find that, depending on the initial conditions, the growing mode may or may not lead to a pancake singularity, analogous to a Zel'dovich pancake. This is in contrast with the $\Lambda =0$ pure Einstein-de-Sitter background where, at any given point in comoving (Lagrangian) coordinates pancakes will always occur.

20 pages, 4 figures, some changes made in the text, 4 references added and Eqs. (46) and (C3) corrected

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• Lagrangian theory of structure formation in relativistic cosmology II: average properties of a generic evolution model
• A novel approach to the dynamics of Szekeres dust models
• Redshift and distances in a ΛCDM cosmology with non-linear inhomogeneities
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• Vorticity and entropy production in tilted Szekeres spacetimes
• Multiple non-spherical structures from the extrema of Szekeres scalars
• Light propagation through black-hole lattices
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• Frame Rotation in the Szekeres Spacetimes
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