The Cosmic Web

The cosmic web is the largest structural pattern known in nature. Galaxies, gas, and dark matter are woven into a complex weblike structure on scales of a few up to a hundred megaparsec, forming dense compact clusters, elongated filaments, and sheetlike walls surrounding near-empty void regions. The complex connectivity and intrinsic multiscale character of the cosmic web reflect the primordial conditions out of which the structural elements of the universe have emerged through non-linear gravitational evolution.

Modern surveys capture the cosmic matter distribution with unprecedented precision, and the complex weblike structure can be readily reproduced in N-body simulations. Yet, a theoretical understanding of the emergent complexity from the underlying structure formation processes remains elusive.

Remarkably, the geometry of the cosmological structure formation can be rigorously understood in the mathematical framework of catastrophe theory (e.g. Arnol'd et al. (1985)), which reveals that the collapsing structure may be classified in terms of caustics in the dark matter flow. The caustic skeleton of the cosmic web goes back to the seminal work of Arnol'd, Shandarin and Zel'dovich (1982), but it was only recently that Feldbrugge et al. (2018) provided an exhaustive list of caustic conditions for the formation of the cosmic web in the realistic three-dimensional universe.

This PhD thesis will build on and further develop this formalism in order to investigate the cosmic web from an unprecedented analytical perspective.

Several projects studying different aspects of the caustic skeleton model of the cosmic web are envisaged. Firstly, we will use the caustic conditions to set up constrained random initial conditions for specialised N-body simulations. This will allow us to infer the characteristic geometries and physical observables of the different structural elements.

Moreover, random field theory enables a systematic investigation of their number densities and correlation functions as imprinted in the primordial initial conditions. As far as the formalism is concerned, this thesis will also study the influence of more general cosmological structure formation models on the evolving caustic network, which can be directly compared to traditional and community-standard identification methods for the cosmic web.

In a broader context, this will also pave the way for novel machine learning techniques for analysing cosmological large-scale structure in next-generation inference pipelines.