The Local Theory of the Cosmic Skeleton

TL;DR

This paper develops a local theoretical framework for analyzing the critical lines that form the filamentary skeleton of cosmic structures in Gaussian fields, providing analytical predictions and classifications of these features.

Contribution

It introduces a new local theory for the critical lines of Gaussian fields, linking skeleton properties to Gaussian curvature and classifying singular points.

Findings

The stiff approximation accurately predicts the shape of the differential length of critical lines.

Analytical solutions for the skeleton's properties are derived.

The theory's predictions match measurements in Gaussian random field realizations.

Abstract

The local theory of the critical lines of 2D and 3D Gaussian fields that underline the cosmic structures is presented. In the context of cosmological matter distribution the subset of critical lines of the 3D density field serves to delineate the skeleton of the observed filamentary structure at large scales. A stiff approximation used to quantitatively describe the filamentary skeleton shows that the flux of the skeleton lines is related to the average Gaussian curvature of the 1D (2D) sections of the field, much in the same way as the density of the peaks. The distribution of the length of the critical lines with threshold is analyzed in detail, while the extended descriptors of the skeleton - its curvature and its singular points, are introduced and briefly described. Theoretical predictions are compared to measurements of the skeleton in realizations of Gaussian random fields in 2D and 3D. It is found that the stiff approximation predicts accurately the shape of the differential length, allows for analytical insight, and explicit closed form solutions. Finally, it provides a simple classification of the singular points of the critical lines: i) critical points; ii) bifurcation points; iii) slopping plateaux.