Thermal history of the universe

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Table of contents

1 Introduction 
1.1 A brief history of modern Cosmology
1.2 State-of-the-art Cosmology
1.2.1 Dark Matter
1.2.2 Dark Energy
1.3 Plan of the thesis
I Theoretical Cosmology 
2 Cosmological models 
2.1 Distances in cosmology
2.2 Hubble’s law
2.3 Hot Big Bang model
2.3.1 Big Bang singularity
2.3.2 Cosmological horizons
2.3.3 Thermal history of the universe
2.4 Einstein–de Sitter universe
2.5 CDM scenario
2.6 Scalar field models of Dark Energy
2.6.1 Quintessence
2.6.2 K-essence
3 Structure formation 
3.1 Statistical treatment of perturbations
3.2 Linear Perturbation Theory
3.2.1 Power spectrum evolution in linear regime
3.3 Non-linear regime
3.3.1 The Zel’dovich approximation
3.3.2 Spherical collapse
4 Numerical simulations 
4.1 N-body techniques
4.2 Eulerian hydrodynamics
4.3 Generation of initial conditions
4.4 Power spectrum estimation
II Cosmology with large volume galaxy surveys 
5 Cosmological dependence of the large scale structure of the universe 
5.1 Galaxy power spectrum
5.2 Baryon Acoustic Oscillations
5.2.1 Non-linear effects on BAO
5.3 Bayesian methods for cosmological parameter inference
5.3.1 Maximum Likelihood Estimator
5.3.2 Fisher matrix
5.3.3 Information content of galaxy surveys
5.4 Contributions of this thesis
6 Matter power spectrum covariance matrices from the DEUSPUR simulations 
6.1 N-body dataset
6.2 Power Spectrum & Covariance Matrix Estimators
6.3 Numerical Simulation Mass Resolution Errors
6.4 Fourier Mode Correlations
6.5 Probability Distribution of the Power Spectrum Estimator
7 Non-linear covariance matrix errors and cosmological parameter uncertainties for Euclid-like surveys 
7.1 Signal-to-Noise
7.2 Covariance and Precision Matrix Errors
7.2.1 Precision Matrix Bias
7.2.2 Variance of Sample Covariance
7.2.3 Variance of Sample Precision Matrix
7.3 Covariance Estimation Errors and Parameter Forecast
III Numerical methods for Dark Energy simulations
8 Numerical methods for clustering Dark Energy simulations 
8.1 Euler Equations for Dark Energy Fluids
8.2 The Riemann Problem
8.2.1 Generalised Riemann Invariants
8.2.2 Rarefaction Waves
8.2.3 Shock Waves
8.2.4 Exact Riemann Solver
8.2.5 Approximate Riemann Solvers
8.2.6 Specificities of the Riemann Problem for Dark Fluids
8.3 Wave structure in 3D
8.4 Upwind Numerical Schemes
8.4.1 Conservative Hyperbolic Methods
8.4.2 MUSCL-Hancock Method
8.4.3 Piecewise Linear Method (PLM)
8.4.4 Piecewise Parabolic Method (PPM)
8.5 Euler Equations in Supercomoving Variables
8.6 Euler Equations in Spherical Symmetry
9 Future prospects