| dc.description.abstract | The current paradigm of a 6 parameter ΛCDM cosmology with single field slow-roll inflation predicts a perfectly Gaussian and isotropic distribution for the Cosmic Microwave Background (CMB) temperature field. However, several statistical anomalies have been reported in the CMB, calling into question whether other models could more accurately describe the statistical properties of the CMB. In this thesis, we investigate a model proposed by Hansen et al. [1] reproducing the aforementioned anomalies. We work in the basis of wavelets, Spherical Mexican Hat Wavelets (SMHW) and spherical standard needlets, yielding several advantages over the traditional spherical harmonics in the presence of incomplete sky coverage. We simulate a large number of CMB maps, both Gaussian and non-Gaussian realizations as per the model, and estimate the wavelet 4-point correlation function, the trispectrum. The use of the trispectrum is motivated by the presence of scaledependent, non-Gaussian, gNL-like terms in the model. We propose a blind test of non-Gaussianity, a chi^2 statistic testing the Gaussian null hypothesis on the simulated maps. We also propose a method for testing the model hypothesis, an estimator alpha quantifying the amount of contribution from a non-Gaussian term in the CMB maps preferred by the data. In addition, we compare our results with those of the Planck experiment, by applying the same framework to the 2015 Planck FFP8.1 Monte Carlo simulation data. For the spherical standard needlets, the results are consistent with the Gaussian null hypothesis. However, a detection is seen in the Spherical Mexican Hat Wavelets maps, disfavoring the Gaussian null hypothesis at 0.63% significance. | eng |