Probing the Gaussianity and the statistical isotropy of the CMB with spherical wavelets

This article focuses on the study of the statistical properties of the cosmic microwave background (CMB) temperature fluctuations. This study helps to define a coherent framework for the origin of the Universe, its evolution and the structure formation. The current standard model is based in the Big-Bang theory, in the context of the Cosmic Inflation scenario, and predicts that the CMB temperature fluctuations can be understood as the realization of a statistical isotropic and Gaussian random field. To probe whether these statistical properties are satisfied or not is capital, since deviations from these hypotheses would indicate that non-standard models might play an important role in the dynamics of the Universe. But that is not all. There are alternative sources of anisotropy or non-Gaussianity that could contaminate the CMB signal as well. Hence, sophisticated techniques must be used to carry out such a probe. Among all the methodologies that one can face in the literature, those based on wavelets are providing one of the most interesting insights to the problem. Their ability to explore several scales keeping. at the same time, spatial information of the CMB, is a very useful property to discriminate among possible sources of anisotropy and/or non-Gaussianity.