  The gravitino is a promising candidate for cold dark matter. We study
cosmological constraints on scenarios in which the gravitino is the lightest
supersymmetric particle and a charged slepton the next-to-lightest
supersymmetric particle (NLSP). We obtain new results for the hadronic
nucleosynthesis bounds by computing the 4-body decay of the NLSP slepton into
the gravitino, the associated lepton, and a quark-antiquark pair. The bounds
from the observed dark matter density are refined by taking into account
gravitinos from both late NLSP decays and thermal scattering in the early
Universe. We examine the present free-streaming velocity of gravitino dark
matter and the limits from observations and simulations of cosmic structures.
Assuming that the NLSP sleptons freeze out with a thermal abundance before
their decay, we derive new bounds on the slepton and gravitino masses. The
implications of the constraints for cosmology and collider phenomenology are
discussed and the potential insights from future experiments are outlined. We
propose a set of benchmark scenarios with gravitino dark matter and long-lived
charged NLSP sleptons and describe prospects for the Large Hadron Collider and
the International Linear Collider.
