The gravitino is a promising supersymmetric dark matter candidate, even without strict R-parity conservation. In fact, with some small R-parity violation, gravitinos are sufficiently long-lived to constitute the dark matter of the universe, while the resulting cosmological scenario is consistent with primordial nucleosynthesis and the high reheating temperature needed for thermal leptogenesis. Furthermore, in this scenario the gravitino is unstable and might thus be accessible by indirect detection via its decay products. We compute in this thesis the partial decay widths for the gravitino in models with bilinear R-parity breaking. In addition, we determine the neutrino signal from astrophysical gravitino dark matter decays. Finally, we discuss the feasibility of detecting these neutrino signals in present and future neutrino experiments, and conclude that it will be a challenging task. Albeit, if detected, this distinctive signal might bring considerable support to the scenario of decaying gravitino dark matter.
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