Ricerca di Materia Oscura attraverso cross-correlazione tra raggi gamma e CMB lensing

During the discussion of this thesis, we will give an overview about the Dark Matter (DM) problem; in particular we will review the main evidences of the DM presence in the Universe and we will outline the main DM candidates. We will discuss the possible paths of DM detection; in particular we will explain the differences between direct and indirect detection. Then we will focus on indirect detection, which relies on the study of the DM annihilation/decay products. The indirect signals are isotropic at large scale but they contain a subdominant anisotropic component, due to the anisotropic distribution of DM. The central idea of this work is to find with statistical instruments, i.e. the Angular Power Spectrum (APS), a cross-correlation signal between the extragalactic DM induced anisotropies in the electromagnetic emission and some gravitational tracer. We have chosen, from one side, the gamma-ray signal and the CMB weak lensing effect, from the other side. Thus, we will give a review of the APS formalism and we will discuss the ingredients which are necessary to its computation. We will show some results of the cross-correlation computation and outline the main diffences between the annihilating and decaying case and the possible annihilation/decay channels. A cross-correlation between the gamma-ray extragalactic emission and CMB weak lensing has already been measured with a 3 sigma confidence level; we will explicitely discuss the ensuing implication for DM, which have not been derived in the original study, such as cross-section/decay time best fit values and constraints on DM features, by comparing our computation results and the data.