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We test the statistical isotropy and Gaussianity of the cosmic microwave background (CMB) anisotropies using observations made by the Planck satellite. Our results are based mainly on the full Planck mission for temperature, but also include some polarization measurements. In particular, we consider the CMB anisotropy maps derived from the multi-frequency Planck data by several component-separation methods. For the temperature anisotropies, we find excellent agreement between results based on these sky maps over both a very large fraction of the sky and a broad range of angular scales, establishing that potential foreground residuals do not affect our studies. Tests of skewness, kurtosis, multi-normality, N-point functions, and Minkowski functionals indicate consistency with Gaussianity, while a power deficit at large angular scales is manifested in several ways, for example low map variance. The results of a peak statistics analysis are consistent with the expectations of a Gaussian random field. The “Cold Spot” is detected with several methods, including map kurtosis, peak statistics, and mean temperature profile. We thoroughly probe the large-scale dipolar power asymmetry, detecting it with several independent tests, and address the subject of a posteriori correction. Tests of directionality suggest the presence of angular clustering from large to small scales, but at a significance that is dependent on the details of the approach. We perform the first examination of polarization data, finding the morphology of stacked peaks to be consistent with the expectations of statistically isotropic simulations. Where they overlap, these results are consistent with the Planck 2013 analysis based on the nominal mission data and provide our most thorough view of the statistics of the CMB fluctuations to date.

[ES]: Durante las últimas décadas, las grandes colaboraciones, la innovación tecnológica y una dosis de creatividad han permitido que el conocimiento del Universo creciera considerablemente, dando lugar a un modelo estándar para explicar el contenido del Universo y su evolución. Las observaciones de alta precisión han sido y serán muy importantes para obtener una imagen detallada del Universo. Gran parte de la información cosmológica ha sido obtenida del estudio del fondo cósmico de microondas, de la estructura a gran escala y supernovas de tipo Ia. Durante los próximos años, se espera obtener información valiosa de observaciones del efecto lente débil, oscilaciones acústicas de bariones y de la polarización del fondo cósmico de microondas. Este tesis se centra en dos de estos temas, el fondo cósmico de microondas y el efecto lente débil. El objetivo de esta tesis es contribuir con nuevas herramientas al análisis de estos observables para obtener la mayor información posible de una manera simple y computacionalmente eficiente., [EN]: During the past few decades, large collaborations, technology innovation and a dose of creativity has led the knowledge of our Universe to grow considerably, giving rise to a standard model to explain the Universe content and evolution. The high precision cosmological observations have been and will be very important to obtain a detailed picture of our Universe. The most notable cosmological information has been obtained from the cosmic microwave background (CMB), large scale structure distribution and supernovae Ia observations. During the next years the cosmological history should be continued with observations of weak lensing, baryonic acoustic oscillations and CMB polarization surveys, among other probes. The PhD thesis presented here is focused on two of these topics, CMB and weak lensing. for future experiments are very The aim of this thesis is to contribute with new tools to the analysis of those observables in order to extract the largest amount of information possible in a simple and computationally efficient way.

We investigate the extent to which cosmic size magnification may be used to complement cosmic shear in weak gravitational lensing surveys, with a view to obtaining high-precision estimates of cosmological parameters. Using simulated galaxy images, we find that unbiased estimation of the convergence field is possible using galaxies with angular sizes larger than the point spread function (PSF) and signal-to-noise ratio in excess of 10. The statistical power is similar to, but not quite as good as, cosmic shear, and it is subject to different systematic effects. Application to ground-based data will be challenging, with relatively large empirical corrections required to account for the fact that many galaxiesare smaller than the PSF, but for space-based data with 0.1-0.2 arcsec resolution, the size distribution of galaxies brighter than i≃24 is almost ideal for accurate estimation of cosmic size magnification. © 2013 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.

A new method to constrain the local non-linear coupling parameter fNL based on a fast wavelet decomposition is presented. Using a multiresolution wavelet adapted to the HEALPix pixelization, we have developed a method that is ∼102 times faster than previous estimators based on isotropic wavelets and ∼103 faster than the KSW bispectrum estimator, at the resolution of theWilkinson Microwave Anisotropy Probe (WMAP) data. The method has been applied to theWMAP7-yrV+Wcombined map, imposing constraints on fNL of−69 < fNL < 65 at the 95 per cent CL. This result has been obtained after correcting for the contribution of the residual point sources which has been estimated to be fNL = 7 ± 6. In addition, a Gaussianity analysis of the data has been carried out using the third-order moments of the wavelet coefficients, finding consistency with Gaussianity. Although the constraints imposed on fNL are less stringent than those found with optimal estimators, we believe that a very fast method, as the one proposed in this work, can be very useful, especially bearing in mind the large amount of data that will be provided by future experiments, such as the Planck satellite. Moreover, the localization of wavelets allows one to carry out analyses on different regions of the sky. As an application, we have separately analysed the two hemispheres defined by the dipolar modulation proposed by Hoftuft et al. We do not find any significant asymmetry regarding the estimated value of fNL in those hemispheres.