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Cosmology and the Galaxy-Matter Connection Using Weak Gravitational Lensing Cross-Correlations in the Dark Energy Survey

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Cosmology and the Galaxy-Matter Connection Using Weak Gravitational Lensing Cross-Correlations in the Dark Energy Survey ADVERTIMENT. Lʼaccés als continguts dʼaquesta tesi queda condicionat a lʼacceptació de les condicions dʼús establertes per la següent llicència Creative Commons: http://cat.creativecommons.org/?page_id=184 ADVERTENCIA. El acceso a los contenidos de esta tesis queda condicionado a la aceptación de las condiciones de uso establecidas por la siguiente licencia Creative Commons: http://es.creativecommons.org/blog/licencias/ WARNING. The access to the contents of this doctoral thesis it is limited to the acceptance of the use conditions set by the following Creative Commons license: https://creativecommons.org/licenses/?lang=en Cosmology and the galaxy-matter connection using weak gravitational lensing cross-correlations in the Dark Energy Survey Judit Prat Martí Tesi Doctoral Programa de Doctorat en Física Director: Dr. Ramon Miquel Pascual Departament de Física Facultat de Ciències Universitat Autònoma de Barcelona 2019 Contents Introduction and Motivation 1 I Preliminars 5 1 Cosmological background 7 1.1 The cosmological principle and the expanding universe ........ 7 1.2 The metric of the Universe ........................ 8 1.3 Redshift and the Hubble Law ....................... 9 1.4 The Cosmic Microwave Background .................. 11 1.5 The Standard Cosmological Model .................... 13 1.6 Distances .................................. 17 1.6.1 Angular diameter distance .................... 17 1.6.2 Luminosity distance ....................... 18 1.7 The Inhomogeneous Universe ...................... 19 1.7.1 Structure Formation ....................... 19 1.7.2 Statistics of the matter density field ............... 20 1.7.3 Evolution of the density field .................. 24 1.7.4 Galaxy bias ............................ 26 2 Weak Gravitational Lensing 29 2.1 Light propagation and the deflection angle ............... 29 2.1.1 The lens equation ......................... 31 2.1.2 Lensing potential ......................... 32 2.2 Linearised lens mapping: Shear and magnification ........... 34 2.3 Measurement of galaxy shapes and estimation of shear ......... 37 2.3.1 Spherical Distribution: Tangential and Cross Components of the Shear ............................. 38 2.4 Galaxy-galaxy lensing ........................... 42 iii CONTENTS 2.5 Cosmological weak lensing ........................ 43 2.5.1 Generalization of the lensing potential ............. 44 2.5.2 Convergence as the projected matter density .......... 44 2.5.3 Projected densities for the foreground distribution ...... 45 2.5.4 Angular correlation function and angular power spectrum .. 46 2.5.5 Modeling of the tangential shear ................ 48 2.6 CMB Lensing ............................... 50 3 The Dark Energy Survey 55 3.1 Redshift estimation ............................ 59 3.2 Shape estimation ............................. 61 II Galaxy bias 65 4 Galaxy bias from galaxy-galaxy lensing in the DES Science Verification Data 67 4.1 Introduction ................................ 67 4.2 Theory and method ............................ 70 4.3 Description of the data .......................... 71 4.3.1 The lenses: The Benchmark sample ............... 71 4.3.2 The Sources: Shape Catalogs .................. 72 4.3.3 Photometric redshifts ...................... 73 4.3.4 Veto Mask ............................. 75 4.4 Measurement methodology ........................ 76 4.4.1 Measurement of the tangential shear and the cross-component 76 4.4.2 Covariance matrix ........................ 77 4.4.3 Galaxy bias estimation ...................... 79 4.4.4 Non-linear bias model ...................... 82 4.5 Results ................................... 83 4.5.1 Tangential shear measurements ................. 83 4.5.2 Galaxy bias results ........................ 84 4.6 Systematic effects in galaxy-galaxy lensing ............... 86 4.6.1 Cross-component and tangential shear around random points 86 4.6.2 Photometric redshift errors ................... 87 4.6.3 Reduced shear and magnification ................ 88 4.6.4 Multiplicative shear biases .................... 89 4.6.5 Intrinsic alignments ....................... 89 4.6.6 Splitting sources in redshift ................... 90 4.6.7 Observational systematic effects ................. 90 iv CONTENTS 4.7 Discussion and Comparison to previous work ............. 91 4.7.1 Non-linear bias .......................... 94 4.7.2 Stochasticity ........................... 95 4.7.3 Fiducial cosmology dependence ................. 95 4.7.4 Photo-z errors and systematics ................. 96 III Galaxy-galaxy lensing to probe cosmology 99 5 Dark Energy Survey Year 1 Results: Galaxy-Galaxy Lensing 101 5.1 Introduction ................................ 101 5.2 Theory ................................... 103 5.3 Data and simulations ........................... 105 5.3.1 Lens sample: redMaGiC ..................... 105 5.3.2 Source samples: Metacalibration and im3shape ....... 106 5.3.3 Photometric redshifts for the source sample .......... 106 5.3.4 Lognormal simulations ..................... 107 5.4 Measurement and covariance ....................... 108 5.4.1 Measurement methodology ................... 108 5.4.2 Measurement results ....................... 112 5.4.3 Covariance matrix validation .................. 113 5.5 Data systematics tests ........................... 115 5.5.1 Cross-component ........................ 118 5.5.2 Impact of PSF residuals ..................... 118 5.5.3 Size and S/N splits ........................ 120 5.5.4 Impact of observing conditions ................. 121 5.6 Shear-Ratio test .............................. 124 5.6.1 Testing the method on simulations ............... 126 5.6.2 Application to data ........................ 127 5.7 redMaGiC galaxy bias ........................... 132 5.8 Conclusions ................................ 135 6 Dark Energy Survey Year1 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing 137 6.1 Introduction ................................ 137 6.2 Two-point measurements and modeling ................. 140 6.2.1 Galaxy Clustering: w(θ) ..................... 140 6.2.2 Galaxy–galaxy lensing: γt(θ) .................. 142 6.2.3 Cosmic shear: ξ±(θ) ....................... 143 6.3 Inferring cosmological parameters .................... 143 v CONTENTS 6.3.1 Likelihood analysis ........................ 145 6.4 DES Y1 3x2pt Cosmological Results and Conclusions ......... 146 IV Cosmological Constraints from Lensing Ratios 149 7 Cosmological lensing ratios with DES Y1, SPT and Planck 151 7.1 Introduction ................................ 151 7.2 Formalism ................................. 153 7.3 Data .................................... 156 7.3.1 Tracer galaxies .......................... 156 7.3.2 Galaxy lensing convergence maps ................ 157 7.3.3 CMB lensing map ........................ 158 7.4 Measurements of the lensing ratios ................... 158 7.4.1 Measuring the tracer-lensing two-point functions ....... 159 7.4.2 Covariance matrix of the two-point functions ......... 159 7.4.3 Correcting the two-point functions for thermal Sunyaev-Zel’dovich contamination .......................... 160 7.4.4 Extracting constraints on the lensing ratios .......... 161 7.5 Modeling the lensing ratios ........................ 162 7.5.1 Modeling photometric redshift and shear calibration bias . 162 7.5.2 Complete model for the lensing ratio .............. 163 7.5.3 Model Validation ......................... 163 7.6 Results ................................... 166 7.6.1 Correlation function and ratio constraints ........... 167 7.6.2 Cosmological constraints .................... 168 7.7 Forecasts .................................. 170 7.7.1 Calculation of projected uncertainty .............. 170 7.7.2 Future experiment configuration ................ 172 7.7.3 Future constraints on lensing ratios ............... 174 7.7.4 Impact of systematic errors on lensing ratios .......... 177 7.8 Conclusions ................................ 179 Summary and conclusions 181 A ΔΣ and γt 183 B Effect of random point subtraction in the tangential shear measurement187 C Metacalibration responses scale dependence 191 vi CONTENTS D Test of Gaussian approximation to ratio posteriors 193 Bibliography 195 vii Introduction and Motivation Cosmology is the study of the origin, evolution and fate of the Universe. The Uni- verse is not static and in 1929 Edwin Hubble discovered it is expanding, which is under- stood as a natural consequence of the Big Bang. Also, since Albert Einstein developed his theory of General Relativity in 1915, we know that the geometry and the dynamics of the Universe are governed by its content. In particular, the total energy density of the Universe dictates its geometry, whether it is flat, open or closed, while its dynamics is determined by the fractional densities of the different forms of energy present in it. If we are able to know the evolution of the energy density of each component of the Universe from the Big Bang until today, we will be able to predict how the Universe will evolve in the future and its ultimate fate. That is why measuring the content of the Universe and its evolution with high precision has become one of the major goals of modern cosmology and in particular one of the motivations for this thesis. Observations made during the previous century have enabled major advancements in the field. They indicated that the components of the Universe that have dominated its energy density are radiation at early times and matter after that (mostly dark matter), clustered
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