Indirect detection of Dark Matter with neutrinos

In this doctoral thesis, we discuss indirect Dark Matter detection with neutrinos. We perform a detailed calculation of the neutrino spectra coming from Dark Matter annihilations inside the Sun and the Earth, taking into account all the possible processes that could occur during propagation: oscillation and interaction with matter. We examine in a systematic way the possibilities of Dark Matter annihilation directly into neutrinos, considering the case of scalar and fermionic Dark Matter. We explicitly calculate the annihilation cross section for different typologies of diagrams. We identify the most favourable scenarios, for which the behaviour of the cross section is given. We then describe the phenomenology of the leptophilic Dark Matter and show how experimental bounds on the neutrino flux coming from annihilations inside the Sun disfavour this model as explanation of the DAMA results. Finally, a carefull analysis of the neutrino flux expected from neutralino annihilations inside the Sun and the Earth is presented. We consider uncertainties coming from both particle physics and astrophysics and we divide the fluxes in through-going and stopping muons