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The Cosmic Microwave Background Radiation at Large Scales and the Peak Theory

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The Cosmic Microwave Background Radiation at Large Scales and the Peak Theory UNIVERSIDAD DE CANTABRIA La radiaci´ondel fondo c´osmicode microondas a gran escala y la teor´ıade picos por Airam Marcos Caballero Memoria presentada para optar al t´ıtulode Doctor en Ciencias F´ısicas en el Instituto de F´ısicade Cantabria Abril 2017 Declaraci´onde Autor´ıa Enrique Mart´ınezGonz´alez, doctor en ciencias f´ısicasy profesor de investigaci´ondel Consejo Superior de Investigaciones Cient´ıficas, y Patricio Vielva Mart´ınez, doctor en ciencias f´ısicasy profesor contratado doctor de la Universidad de Cantabria, CERTIFICAN que la presente memoria, La radiaci´ondel fondo c´osmicode microondas a gran scala y la teor´ıade picos ha sido realizada por Airam Marcos Caballero bajo nuestra direcci´onen el Instituto de F´ısicade Cantabr´ıa,para optar al t´ıtulode Doctor por la Universidad de Cantabria. Consideramos que esta memoria contiene aportaciones cient´ıficassuficientes para cons- tituir la Tesis Doctoral del interesado. En Santander, a 7 de abril de 2017, Enrique Mart´ınezGonz´alez Patricio Vielva Mart´ınez iii Agradecimientos Ciertamente, esta tesis no podr´ıahaber sido posible sin la ayuda, apoyo, trabajo y con- sejos de mis dos directores, Enrique y Patricio. Gracias a ellos he podido adentrarme en el mundo de la cosmolog´ıa,incluso en regiones que van mucho m´asall´ade lo presentado en esta tesis. Muchas gracias por todo este tiempo en el que no he dejado de aprender. No ser´ıajusto empezar estos agradecimientos sin mencionar tambi´ena los organismos que me han dado cobijo y apoyo econ´omico: el Instituto de F´ısica de Cantabria, la Universidad de Cantabria, el Consejo Superior de Investigaciones Cient´ıficasy el Minis- terio de Econom´ıay Competitividad. Detr´asde todas estas instituciones se encuentra la imprescindible aportaci´onde los contribuyentes, los mecenas de nuestro tiempo que permiten los avances cient´ıficos.En parte, esta tesis tambi´enes de todos ellos. Por supuesto, tambi´entengo que agradecer a mis compa~neros(no solo de despacho) por todos estos a~nos.Las discusiones y debates, cient´ıficoso no, son muchas veces la base y el germen de nuevas ideas y perspectivas. Gracias a Ra´ulpor aguantar mis desvar´ıos y aportar ese contrapeso que equilibria la balanza del m´etodo cient´ıfico,cuestionando hasta el m´aspeque~nodetalle. A Biuse, tambien conocida por ser la reina de Altamira, por ser fuente de inspiraci´on,eficiencia y, sobretodo ahora que es madre, todo un ejemplo de mujer cient´ıfica.Tamb´ıenhe apredido muchas cosas de David, al que cari~nosamente apodo \el ingeniero". Gracias por ense~narmecomo funcionan todos esos cacharros. C´omoolvidar en estas l´ıneasa \el gran chorbo", Luis Fernando, que nos dej´oel legado de las generaciones anteriores de doctorandos. Tambi´ena Andr´esCurto, expatriado en \la p´erfidaAlbi´on",donde parece que ha construido su nuevo hogar (qu´egran cient´ıfico pierde este pa´ıs). No solo de ciencia vive el hombre, y por ello mi m´ascari~nosoagradecimiento es para mi familia y amigos. Empezando por mis abuelos, que han sido y son un gran ejemplo de vida. A mi madre, por ser ese gran apoyo imprescindible e incondicional, y a mi padre, por inculcarme la curiosidad por la ciencia desde peque~no.A mi hermana, que no por ser la ´unica que tengo deja de ser la mejor. Tambi´ena Carmen, Fernando y Vero, por hacer m´asgrande esta familia y compartir muchos buenos momentos juntos. Tambi´entengo que agradecer a muchos amigos y personas cercanas, a los que no nombro personalmente por el miedo a dejarme alguno de ellos. Gracias a todos ellos. Y, c´omo no, a Andrea, por estar siempre ah´ı,d´andometodo su apoyo y compartiendo conmigo todos los buenos y los malos momentos. UNIVERSIDAD DE CANTABRIA The Cosmic Microwave Background radiation at large scales and the peak theory by Airam Marcos Caballero A thesis submitted in partial fulfillment for the degree of Doctor of Philosophy in Physics in the Instituto de F´ısicade Cantabria April 2017 Abstract In this PhD thesis, the large-scale anisotropies in the Cosmic Microwave Background (CMB) radiation are analysed. In particular, the theory of peaks in a Gaussian random field on the sphere is reviewed and applied to the CMB temperature and polarization fields, including the eccentricity of the peaks in the formalism. Previous to the charac- terization of the large-scale peaks, a general study of the derivatives up to second order of the Planck CMB temperature data is performed at different scales, identifying the most significant deviations from the standard cosmological model prediction. A more detailed anaylsis is applied to the largest peaks on the CMB temperature and the Cold Spot. The formalism of the multipolar profiles is used to characterize the shape and ge- ometry of those peaks. Finally, the large-scale anisotropies produced by the Integrated Sachs-Wolfe (ISW) effect are analysed in the last two chapters. In the first one, the claim that the Cold Spot can be originated by the imprint on the CMB temperature of a su- pervoid is analysed, considering different dark energy models and void geometries. On the other hand, in the last chapter, the ISW effect is detected from the cross-correlation between the CMB temperature and large-scale structure tracers. In particular, the red- shift distribution and angular power spectrum of the NRAO VLA Sky Survey (NVSS) are studied in order to have a theoretical model of the angular cross-power spectrum between the CMB temperature and this galaxy catalogue. Some results presented in the latter chapter are included in the publications of the Planck collaboration on the integrated Sachs-Wolfe effect. Contents Declaraci´onde Autor´ıa iii Agradecimientosv Abstract ix List of Figures xv List of Tables xvii Abbreviations xix Physical Constants xxi Symbols xxiii 1 Introduction1 1.1 The standard cosmological model.......................2 1.1.1 The Friedmann equations.......................2 1.1.2 Cosmic fluid and the Universe dynamics...............5 1.1.3 Energetic components of the Universe................ 10 1.1.4 Cosmological perturbations...................... 16 1.2 Inflation..................................... 19 1.2.1 Problems of the classical Big Bang model.............. 21 1.2.2 Physics of inflation........................... 23 1.2.3 Initial perturbations from inflation.................. 25 1.3 Cosmic Microwave Background........................ 29 1.3.1 The CMB angular power spectra................... 30 1.3.2 CMB physics.............................. 32 1.3.3 CMB observations........................... 41 1.3.4 CMB anomalies and beyond the standard model.......... 44 2 The shape of CMB temperature and polarization peaks on the sphere 49 2.1 Introduction................................... 49 2.2 Derivatives of a scalar field on the sphere.................. 51 2.3 Uncorrelating the peak variables....................... 53 2.4 Extrema statistics............................... 55 xi Contents xii 2.5 Multipolar profiles............................... 58 2.5.1 Profiles in harmonic space....................... 59 2.5.2 Profiles in real space.......................... 64 2.5.3 Bias discussion............................. 69 2.6 Covariance of the multipolar profiles..................... 70 2.7 Physical interpretation of the peak patterns................. 74 2.8 Peak simulations................................ 76 3 Multiscale analysis of the CMB temperature derivatives 79 3.1 Introduction................................... 79 3.2 Theoretical framework............................. 81 3.3 Data processing................................. 82 3.4 Pixel covariance in the presence of a mask.................. 84 3.5 Covariance of the derivatives......................... 85 3.6 Extreme deviations in the derivatives fields................. 88 3.7 Directional analysis............................... 92 4 Local properties of the large-scale peaks of the CMB temperature 97 4.1 Introduction................................... 97 4.2 Characterization of the large-scale peaks................... 98 4.3 Multipolar profiles............................... 102 4.4 Phase correlations of the multipolar profiles................. 106 4.5 Real space analysis............................... 110 5 On the void explanation of the Cold Spot 115 5.1 Introduction................................... 115 5.2 The void influence on the CMB........................ 116 5.2.1 Spherical model............................. 117 5.2.2 Ellipsoidal model............................ 120 5.2.3 Varying w in the dark energy equation of state........... 122 6 Cross-correlation between the CMB and LSS tracers 125 6.1 Halo mass function and galaxy bias...................... 126 6.2 Galaxy angular power spectrum........................ 128 6.3 Modelling of the NRAO VLA Sky Survey.................. 130 6.4 Estimation of the angular cross-correlation signal from several LSS tracers 135 6.5 Detection of the Integrated Sachs-Wolfe effect from Planck and LSS data 138 7 Conclusions 143 7.1 Chapter 2.................................... 143 7.2 Chapter 3.................................... 145 7.3 Chapter 4.................................... 147 7.4 Chapter 5.................................... 148 7.5 Chapter 6.................................... 149 7.6 Future work................................... 150 Contents xiii A Peaks formalism 153 A.1 Covariant derivatives on the sphere...................... 153 A.2 Peak degrees of freedom............................ 155 A.3 Flat approximation............................... 157 B Integrals of the spin-weighted spherical harmonics 159 C Binning of the
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