A non-linear approximation for perturbations in \Lambda CDM

TL;DR

This paper introduces a non-linear gradient series expansion method to model inhomogeneities in a DM universe, effectively capturing gravitational evolution beyond standard perturbation theory and matching exact solutions even during collapse.

Contribution

It presents a novel non-linear approximation technique using gradient expansion that accurately models inhomogeneities in DM cosmology beyond traditional perturbative limits.

Findings

Gradient expansion describes inhomogeneities well into the non-linear regime.

The method closely matches exact DM solutions during structure formation.

It remains accurate through collapse into singularities.

Abstract

We describe inhomogeneities in a {\Lambda}CDM 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 {\Lambda}LTB solutions (Lema\^itre-Tolman-Bondi metric with the inclusion of a cosmological constant) describing growing structure in a {\Lambda}CDM universe and find that the expansion approximates the exact solution well, following the collapse of an over-density all the way into a singularity.