Cosmic Web & Caustic Skeleton: non-linear Constrained Realizations -- 2D case studies

TL;DR

This paper introduces a formalism for setting up non-linearly constrained initial conditions in cosmological simulations, linking initial density fields to the evolved cosmic web structures like filaments and clusters.

Contribution

It extends constrained Gaussian random field theory and the Hoffman-Ribak algorithm to incorporate non-linear constraints based on caustic skeleton theory, enabling detailed study of cosmic web progenitors.

Findings

Developed a nonlinear constrained random field theory applicable to cosmology.

Applied the method to 2D case studies demonstrating its effectiveness.

Facilitated systematic investigation of cosmic web evolution from initial conditions.

Abstract

The cosmic web consists of a complex configuration of voids, walls, filaments, and clusters, which formed under the gravitational collapse of Gaussian fluctuations. Understanding under what conditions these different structures emerge from simple initial conditions, and how different cosmological models influence their evolution, is central to the study of the large-scale structure. Here, we present a general formalism for setting up initial random density and velocity fields satisfying non-linear constraints for specialized N-body simulations. These allow us to link the non-linear conditions on the eigenvalue and eigenvector fields of the deformation tensor, as specified by caustic skeleton theory, to the current-day cosmic web. By extending constrained Gaussian random field theory, and the corresponding Hoffman-Ribak algorithm, to non-linear constraints, we probe the statistical properties of the progenitors of the walls, filaments, and clusters of the cosmic web. Applied to cosmological N-body simulations, the proposed techniques pave the way towards a systematic investigation of the evolution of the progenitors of the present-day walls, filaments, and clusters, and the embedded galaxies, putting flesh on the bones of the caustic skeleton. The developed nonlinear constrained random field theory is valid for generic cosmological conditions. For ease of visualization, the case study presented here probes the two-dimensional caustic skeleton.