The role of the environment in shaping galaxies and clusters

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Table of contents

I Emergence of large-scale structures 
1 Structure formation in the Universe 
1.1 The homogeneous universe
1.1.1 Distances in an expanding universe
1.1.2 The dynamics of the homogeneous Universe
1.2 The birth of large-scale structures
1.2.1 Linear perturbation theory
1.2.2 Zel’dovich formalism
1.3 Statistical descriptions of the matter distribution
1.3.1 Discrete random elds
1.3.2 Correlation functions and poly-spectra
1.4 The CDM model
1.4.1 Presentation of the model
1.4.2 Cosmological parameters and matter power spectrum
2 Large-scale structures manifestation 
2.1 Large-scale structures in simulations
2.1.1 First exhibitions
2.1.2 Dark matter only and hydrodynamical simulations
2.2 The cosmic web through galaxies
2.2.1 Galaxy surveys
2.2.2 Observational eects
2.2.3 Galaxy bias
2.3 Motivations for cosmic web classication
2.3.1 The limitations of statistical analyses
2.3.2 The cosmological sensitivity of environments
2.3.3 The role of the environment in shaping galaxies and clusters
2.4 Challenges in detecting cosmic laments
2.4.1 Structural complexity of the pattern
2.4.2 Non-unicity of the denition
2.5 Conclusions and perspectives for the thesis
II Statistical methods for pattern extraction 
3 Statistical physics for clustering 
3.1 Context and motivation
3.1.1 Machine learning and physics
3.1.2 Optimisation problems and regularisation
3.1.3 Clustering and its drawbacks
3.2 Mixture models
3.2.1 General formalism
3.2.2 The Gaussian case
3.3 Expectation-Maximisation algorithm
3.3.1 Introduction through Mixture Models
3.3.2 Iterative scheme
3.3.3 The particular case of Gaussian mixtures
3.4 Phase transitions in Gaussian mixtures
3.4.1 Statistical physics formulation of clustering
3.4.2 From paramagnetic to condensation phase
3.4.3 Hard annealing
3.4.4 Soft annealing
3.4.5 Graph-regularised mixture model
3.5 Summary and prospects
4 Principal graph learning 
4.1 Context
4.1.1 Spatially structured point-cloud data
4.1.2 Principal curves
4.2 Elements of graph theory
4.2.1 Introduction and denitions
4.2.2 Linear algebra representations
4.2.3 Some graph constructions
4.3 Graph regularised mixture models
4.3.1 Full model and formalism
4.3.2 Algorithm and illustrative results
4.4 About graph priors
4.4.1 Basic graph constructions
4.4.2 The average graph prior
4.5 Convergence and time complexity
4.5.1 Convergence analysis
4.5.2 Time complexity
4.5.3 Runtimes
4.6 Hyper-parameters and initialisation
4.6.1 The impact of parameters
4.6.2 Initialisation
4.7 Illustrative application: Road network
4.8 Summary and prospects
III Analysis of the CosmicWeb pattern 
5 The principal graph of the CosmicWeb 
5.1 Context and motivations
5.2 Filamentary pattern detection
5.2.1 T-ReX: Tree-based Ridge eXtractor
5.2.2 Filamentary pattern extraction from Illustris subhalos
5.2.3 Performance evaluation
5.3 Identication of individual laments
5.3.1 A graph-based denition for laments
5.3.2 Characteristics of individual laments
5.3.3 Association of galaxies
5.4 Filaments characteristics in simulations
5.4.1 Simulations and principal graphs
5.4.2 Comparison of laments characteristics
5.5 The impact of the cosmic web on cluster properties in simulations
5.5.1 Data, lamentary pattern and connectivity
5.5.2 Impact of connectivity on the growth and shapes of clusters
5.5.3 Impact of cluster dynamical states on the connectivity
5.5.4 The inuence of mass growth history
5.6 Summary and perspectives
6 Constraining cosmological parameters with cosmic environments 
6.1 Context and introduction
6.1.1 The matter power spectrum as a cosmological probe
6.1.2 The cosmic environments as an alternative probe
6.2 Data & Methodology
6.2.1 The Quijote suite of simulations
6.2.2 Cosmic web segmentation
6.3 Environments sensitivity to cosmology
6.3.1 Cosmic fractions as a function of cosmological parameters
6.3.2 Power spectra in cosmic environments
6.4 Constraining power of cosmic environments
6.4.1 Fisher formalism for information content quantication
6.4.2 Real-space auto-spectra
6.4.3 Redshift-space auto-spectra
6.4.4 Stability and convergence analysis
6.5 Conclusion and perspectives