  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.
