  The gravitino is a promising supersymmetric dark matter candidate which does
not require exact R-parity conservation. In fact, even with some small R-parity
breaking, gravitinos are sufficiently long-lived to constitute the dark matter
of the Universe, while yielding a cosmological scenario consistent with
primordial nucleosynthesis and the high reheating temperature required for
thermal leptogenesis. In this paper, we compute the neutrino flux from direct
gravitino decay and gauge boson fragmentation in a simple scenario with
bilinear R-parity breaking. Our choice of parameters is motivated by a proposed
interpretation of anomalies in the extragalactic gamma-ray spectrum and the
positron fraction in terms of gravitino dark matter decay. We find that the
generated neutrino flux is compatible with present measurements. We also
discuss the possibility of detecting these neutrinos in present and future
experiments and conclude that it is a challenging task. However, if detected,
this distinctive signal might bring significant support to the scenario of
gravitinos as decaying dark matter.
