• anisotropic Universe
• Bianchi I metric
• CMB
• lensing
• perturbation theory
• power spectrum

In recent times, the unprecedented sensibility of the cosmological surveys has allowed us to study the Cosmic Microwave Background (CMB) in great detail. In particular, the present major sources of information are given by the CMB anisotropies spectra. Therefore, the secondary effects on such CMB anisotropies have to be calculated with always better precision to compare theory with observation.
For this reason, new physical phenomena like the lensing at next-to-leading order, which were previously neglected because of the insufficient sensitivity of the experiments, must now be taken into account.
In this thesis I consider how the presence of lensing in an anisotropic Universe modifies the temperature anisotropies of the CMB. It was shown how going beyond the Born approximation, considering non-Gaussian deflection angle, gives non-negligible next-to-leading order corrections in an isotropic Universe. The leading correction to the temperature power spectrum due to second order deflection angle gives a null contribution in an isotropic space. On the other hand, with the presence of anisotropies at the background level this contribution needs to be taken into account and it might be non-negligible depending on the model. In this framework I consider the Bianchi I space-time, which describes a homogeneous but anisotropic Universe. To conclude, as a mathematical tool I use the Geodesic Light-Cone (GLC) coordinates, which offer a physical set of coordinates that allows for an easier description of an anisotropic space-time.