A non-linear approximation for perturbations in ΛCDM

Abstract

We describe inhomogeneities in a ΛCDM universe with a gradient series expansion and show that it describes the gravitational evolution far into the non-linear regime and beyond the capacity of standard perturbation theory at any order. We compare the gradient expansion with exact inhomogeneous ΛLTB solutions (Lemaître-Tolman-Bondi metric with the inclusion of a cosmological constant) describing growing structure in a ΛCDM universe and find that the expansion approximates the exact solution well, following the collapse of an over-density all the way into a singularity.

11 pages, 3 figures, matches published version

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• On general-relativistic Lagrangian perturbation theory and its non-perturbative generalization