# Post-collapse perturbation theory in 1D cosmology -- beyond shell-crossing

## TL;DR

This paper introduces a new perturbation theory approach for modeling the gravitational dynamics of large-scale structures in 1D cosmology after shell-crossing, improving accuracy over previous models.

## Contribution

The authors develop a post-collapse perturbation theory with adaptive smoothing to accurately describe multi-stream flows after shell-crossing in 1D cosmology.

## Key findings

- Accurately reproduces power spectrum at small scales
- Effectively models phase-space structures post-shell-crossing
- Outperforms Zel'dovich approximation in simulations

## Abstract

We develop a new perturbation theory (PT) treatment that can describe gravitational dynamics of large-scale structure after shell-crossing in the one-dimensional cosmological case. Starting with cold initial conditions, the motion of matter distribution follows at early stages the single-stream regime, which can, in one dimension, be described exactly by the first-order Lagrangian perturbation, i.e. the Zel'dovich solution. However, the single-stream flow no longer holds after shell-crossing and a proper account of the multi-stream flow is essential for post-collapse dynamics. In this paper, extending previous work by Colombi (2015, MNRAS 446, 2902), we present a perturbative description for the multi-stream flow after shell-crossing in a cosmological setup. In addition, we introduce an adaptive smoothing scheme to deal with the bulk properties of phase-space structures. The filtering scales in this scheme are linked to the next-crossing time in the post-collapse region, estimated from our PT calculations. Our PT treatment combined with adaptive smoothing is illustrated in several cases. Predictions are compared to simulations and we find that post-collapse PT with adaptive smoothing reproduces the power spectrum and phase-space structures remarkably well even at small scales, where Zel'dovich solution substantially deviates from simulations.