## Morphology of the cosmic web

A natural application of Bayesian large-scale structure inference with BORG is a *high-fidelity description of the complex web-like patterns* in cosmic structure.

### Dark matter voids

An interesting aspect is *voids in the dark matter distribution*. In 2014, we produced and analysed constrained catalogues of dark matter voids in the Sloan volume, probing a deeper void hierarchy and than the distribution of galaxies and alleviating the issues due to sparsity and bias (Leclercq *et al*. 2015a). The catalogues have been made publicly available here and on cosmicvoids.net.

*et al*. 2015a.

### The dynamic cosmic web

More generally, BORG infers a wealth of cosmological information that can be used to classify the large-scale structure. Following the *dynamic cosmic web classification* procedure proposed by Hahn *et al.* (2007), we used the tidal field to classify the large-scale structure into four distinct web-types (voids, sheets, filaments, and clusters) and quantify corresponding uncertainties (Leclercq *et al*. 2015b).

*et al*. 2015b.

Within the same project, we also introduced a *new cosmic web classifier, LICH*, to identify structures while taking into account the existence of both potential and vortical flows. Using it as well a set of phase-space techniques resulted in the first *phase-space analysis of the nearby Universe* as probed by the SDSS (Leclercq *et al.* 2017), which was the object of a press release.

### Cosmic web analysis using decision theory and information theory

With Jens Jasche and Benjamin Wandelt, I proposed to use *Bayesian decision theory* for segmenting the cosmic web into different structure types, on the basis of their (previously inferred) probabilities (Leclercq *et al*. 2015c). Surprisingly, our approach is analogous to the analysis of games of chance where the gambler only plays if a positive expected net gain can be achieved based on some degree of privileged information.

In 2016, we *extended the decision problem to the space of cosmic web classifiers* (Leclercq *et al.* 2016). Our framework, based on information theory, accounts for the design aims of different classes of possible applications: parameter inference, model selection, and prediction of new observations. As an illustration, we assessed the relative performance of different classifiers (the T-web, DIVA, and ORIGAMI) for respectively: analysing the morphology of the cosmic web, discriminating dark energy models, and predicting galaxy colours.

*et al.*2016.