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Impacts of Cosmic Inhomogeneities on the CMB: Primordial Perturbations in Two-Field Bouncing Cosmologies and Cosmic Magnetism In

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Impacts of Cosmic Inhomogeneities on the CMB: Primordial Perturbations in Two-Field Bouncing Cosmologies and Cosmic Magnetism In Impacts of cosmic inhomogeneities on the CMB : primordial perturbations in two-field bouncing cosmologies and cosmic magnetism in late-time structures Nadège Lemarchand To cite this version: Nadège Lemarchand. Impacts of cosmic inhomogeneities on the CMB : primordial perturbations in two-field bouncing cosmologies and cosmic magnetism in late-time structures. Cosmology and Extra-Galactic Astrophysics [astro-ph.CO]. Université Paris Saclay (COmUE), 2019. English. NNT : 2019SACLS510. tel-02935128 HAL Id: tel-02935128 https://tel.archives-ouvertes.fr/tel-02935128 Submitted on 10 Sep 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Impacts of cosmic inhomogeneities on the CMB: primordial perturbations in two-field bouncing cosmologies and cosmic magnetism in late-time structures NNT : 2019SACLS510 These` de doctorat de l’Universite´ Paris-Saclay prepar´ ee´ a` l’Universite´ Paris-Sud Ecole´ doctorale n◦127 Astronomie et astrophysique d’Ile-de-France (AAIF) Specialit´ e´ de doctorat : astronomie et astrophysique These` present´ ee´ et soutenue a` Orsay, le 12 decembre´ 2019, par NADEGE` LEMARCHAND Composition du Jury : Nabila Aghanim Directrice de recherche, CNRS (Institut d’Astrophysique Spatiale) Presidente´ Carlos Hernandez-Monteagudo´ Tenure scientist, Centro de Estudios de F´ısica del Cosmos de Rapporteur Aragon´ Hiroyuki Tashiro Associate Professor, Nagoya University (Cosmology Group) Rapporteur Aurelien´ Barrau Professeur des Universites,´ Universite´ Grenoble Alpes (Laboratoire Examinateur de Physique Subatomique et de Cosmologie) Giulio Fabbian Research fellow, University of Sussex (Physics and Astronomy, Examinateur Astronomy Centre) Julien Grain Charge´ de recherche, CNRS (Institut d’Astrophysique Spatiale) Directeur de these` ` ese de doctorat Th 2 Contents Synthèse 7 Introduction 9 I Cosmology: some basics 13 1 The standard model of cosmology: ΛCDM 15 1.1 From General Relativity to cosmology . 15 1.1.1 From the principle of stationary action to Einstein’s equations . 15 1.1.2 Application to the whole Universe: cosmology . 17 1.1.2.1 The symmetries behind the model . 17 1.1.2.2 An expanding Universe . 18 1.1.2.3 The energy content of the Universe . 18 1.2 ΛCDM: a model with only five independent parameters . 20 1.3 Chronology of the Universe . 23 1.4 Limitations of the model . 25 2 The early Universe 27 2.1 The hot Big Bang scenario . 27 2.1.1 A bit of thermodynamics in an expanding Universe . 27 2.1.2 Chronology in the early Universe . 29 2.2 The inflationary paradigm . 30 2.2.1 Motivations: problems of the hot Big Bang scenario . 30 2.2.1.1 Flatness problem or why the Universe is so flat? . 30 2.2.1.2 Horizon problem or why the Universe is so homogeneous? . 32 2.2.1.3 Structure formation problem . 34 2.2.1.4 Relic problem . 34 2.2.2 Solving these problems: the inflationary paradigm . 35 2.2.2.1 Flatness problem . 35 2.2.2.2 Horizon problem . 36 2.2.2.3 Relic problem . 36 2.2.2.4 Duration of inflation . 36 2.2.3 The simplest model: inflation with one scalar field . 37 2.3 Pre-inflationary physics . 41 3 4 CONTENTS 3 Cosmological perturbations 43 3.1 Dynamical equations for the perturbations . 43 3.1.1 Perturbations of the metric: SVT decomposition . 43 3.1.2 Gauge fixing . 44 3.1.3 Perturbations of matter . 45 3.1.4 Equations of motion . 46 3.2 Quantum origin . 48 3.3 Perturbations with two scalar fields . 49 3.3.1 Adiabatic and isocurvature decomposition . 49 3.3.2 Dynamical equations . 51 3.3.3 Quantum initial conditions . 52 3.4 Primordial power spectra: phenomenological parameterisation . 54 4 The CMB: the observable of the early and late-time inhomogeneities 57 4.1 Release of the relic radiation . 57 4.1.1 Recombination . 57 4.1.2 Decoupling . 58 4.2 Spectral properties of the CMB . 59 4.2.1 Best black body ever measured . 59 4.2.2 Spectral distortions y, µ and Yff ....................... 60 4.3 Anisotropies . 61 4.3.1 Primary anisotropies . 62 4.3.1.1 Temperature anisotropies . 62 4.3.1.2 Polarisation anisotropies . 65 4.3.1.3 Correlations: angular power spectrum and higher order statistics 72 4.3.2 Secondary anisotropies . 75 4.3.3 Reconstruction of the angular power spectra . 80 II Primary anisotropies of the CMB 83 5 A quantum theory of gravitation: Loop Quantum Gravity 85 5.1 Theory: a brief introduction to LQG . 85 5.1.1 Why quantising gravity? . 85 5.1.2 Hamiltonian formulation of GR . 86 5.1.2.1 The 3+1 decomposition . 86 5.1.2.2 GR: a totally constrained system . 88 5.1.2.3 Ashtekar’s variables . 89 5.1.3 Quantisation using loops . 90 5.2 Potential footprints of LQG . 91 6 Application to the early Universe: Loop Quantum Cosmology 93 6.1 The Big Bang singularity replaced by a quantum bounce . 94 6.1.1 Semi-classical description of LQC . 94 6.1.2 Modified Friedmann’s equations and bouncing cosmologies . 95 6.2 LQC with one scalar field . 97 6.2.1 Inflation in LQC . 97 6.2.2 Main phases of the bouncing Universe: contraction, bounce and expansion 98 6.2.3 Main classes of cosmic evolution . 100 6.2.4 Probability of inflation . 101 CONTENTS 5 6.3 Cosmic perturbations in bouncing universes . 104 6.3.1 Equations of motion for the perturbations . 104 6.3.1.1 Deformed algebra approach . 104 6.3.1.2 Dressed metric approach . 105 6.3.2 Predicted primordial power spectra . 106 7 LQC with two scalar fields 111 7.1 Motivations . 111 7.2 Background dynamics . 112 7.2.1 Equations of motion . 112 7.2.2 Analytical approximations phase by phase . 113 7.2.2.1 The contraction . 113 7.2.2.2 The bounce . 116 7.2.3 Inflation in two-fields LQC . 120 7.3 Adiabatic and isocurvature scalar perturbations . 124 7.3.1 Coupled equations of motion . 124 7.3.2 Initial conditions during the contraction . 126 III Secondary polarised anisotropies of the CMB 137 8 Faraday Rotation and Faraday Conversion of the CMB photons in large-scale structures 139 8.1 The Faraday Rotation and Conversion mechanisms . 139 8.1.1 Faraday Rotation . 139 8.1.2 Faraday Conversion . 142 8.2 Dark Matter halos . 143 8.2.1 Large-scale structure of dark matter . 143 8.2.2 Baryonic and magnetic content . 144 8.2.2.1 Distribution of free electrons . 145 8.2.2.2 Modeling the magnetic field . 146 8.3 The halo model . 148 8.4 Angular power spectra of the FR and FC effects by large-scale structures . 150 8.5 Impact on the CMB . 154 8.5.1 Secondary polarised anisotropies . 154 8.5.1.1 Secondary V Stokes parameter . 155 8.5.1.2 Secondary E and B modes . 157 8.5.2 Reconstructing the FR angle and FC rate fields . 159 9 Article 163 Conclusion and prospects 183 A The formalism of the Poincaré sphere 193 A.1 Preliminaries . 193 A.2 The Poincaré sphere . 194 A.3 The Stokes parameters . 196 6 CONTENTS Synthèse Le Fond Diffus Cosmologique (FDC) est une sonde cosmologique clé mettant des contraintes étroites sur le modèle ΛCDM de l’Univers. Emis 380000 ans après le big bang, il montre de petites anisotropies en température et en polarisation qui tracent les inhomogénéités cosmiques à différentes époques de l’Univers. En effet, d’une part les anisotropies primaires, imprimées au moment de son émission, donnent accès à la phase d’inflation ayant lieu au tout début de l’Univers et durant laquelle les perturbations primordiales sont générées. D’autre part, les anisotropies secondaires, imprimées depuis lors, tracent les inhomogénéités dans l’Univers récent, qui ont évolué en grandes structures sous l’action de la gravité à partir des inhomogénéités primordiales, et interagissant alors avec le FDC. Ainsi les anisotropies du FDC sont une sonde puissante à la fois de l’origine des inhomogénéités dans l’Univers très jeune, et de leur état évolué dans l’Univers récent. Cette thèse porte sur deux aspects des inhomogénéités: d’abord leur production dans une extension du scénario inflationnaire, puis la prédiction de l’impact des champs magnétiques des grandes structures sur les anisotropies secondaires polarisées du FDC. Malgré ses succès, l’inflation ne résout pas le problème de la singularité initiale du big bang, où l’interaction gravitationnelle pourrait être quantifiée. En Cosmologie Quantique à Boucles (CQB), cette singularité est remplacée par un rebond quantique. La CQB à un champ avec potentiel quadratique a déjà été étudiée et prédit une phase d’inflation suivant le rebond avec une probabilité proche de un. Dans ce cadre, les perturbations primordiales ne sont plus seulement produites pendant l’inflation, mais aussi pendant le rebond et la contraction le précédant. Dans ma thèse, j’ai considéré une extension à deux champs de la CQB avec un champ.
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