Unveiling the singular dynamics in the cosmic large-scale structure

TL;DR

This paper investigates the formation of singular features in the large-scale structure of the universe, focusing on one-dimensional gravitational collapse, and combines analytical methods with high-resolution simulations to understand these phenomena.

Contribution

It introduces a detailed analytical framework for singularities in one-dimensional gravitational collapse and validates it with high-resolution simulations, outlining steps for three-dimensional extension.

Findings

Identification of non-differentiable features in particle acceleration after first crossing

Excellent agreement between analytical predictions and simulations shortly after crossing

Framework outlined for extending methods to three-dimensional structures

Abstract

It is known that the gravitational collapse of cold dark matter leads to infinite-density caustics that seed the primordial dark-matter halos in the large-scale structure. The development of these caustics begins, generically, as an almost one-dimensional phenomenon with the formation of pancakes. Focusing on the one-dimensional case, we identify a landscape of non-differentiable, and thus, singular features in the particle acceleration that emerge after the first crossing of particle trajectories. We complement our fully analytical studies by high-resolution simulations and find outstanding agreement, particularly shortly after the first crossing. We develop the methods in one space dimension but outline briefly the necessary steps for the 3D case.