Unstable Gravitino Dark Matter and Neutrino Flux

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.