Statistics of Caustics in Large-Scale Structure Formation

TL;DR

This paper derives analytical expressions for the spatial statistics of caustics in the large-scale structure of the universe, using the Zeldovich formalism in 1D and 2D, with extensions to non-linear regimes.

Contribution

It provides new analytical tools for understanding the distribution and correlation of caustics in cosmic structure formation, extending to non-linear regimes.

Findings

Derived expressions for caustic number density and correlation in 1D and 2D.

Framework can be extended to 3D and non-linear regimes.

Lays groundwork for future detailed statistical analysis of cosmic web caustics.

Abstract

The cosmic web is a complex spatial pattern of walls, filaments, cluster nodes and underdense void regions. It emerged through gravitational amplification from the Gaussian primordial density field. Here we infer analytical expressions for the spatial statistics of caustics in the evolving large-scale mass distribution. In our analysis, following the quasi-linear Zeldovich formalism and confined to the 1D and 2D situation, we compute number density and correlation properties of caustics in cosmic density fields that evolve from Gaussian primordial conditions. The analysis can be straightforwardly extended to the 3D situation. We moreover, are currently extending the approach to the non-linear regime of structure formation by including higher order Lagrangian approximations and Lagrangian effective field theory.