  The cosmological moduli problem is discussed in the framework of sequestered
sector/anomaly-mediated supersymmetry (SUSY) breaking. In this scheme, the
gravitino mass (corresponding to the moduli masses) is naturally 10 - 100 TeV,
and hence the lifetime of the moduli fields can be shorter than $\sim 1 sec$.
As a result, the cosmological moduli fields should decay before big-bang
nucleosynthesis starts. Furthermore, in the anomaly-mediated scenario, the
lightest superparticle (LSP) is the Wino-like neutralino. Although the large
annihilation cross section means the thermal relic density of the Wino LSP is
too small to be the dominant component of cold dark matter (CDM), moduli decays
can produce Winos in sufficient abundance to constitute CDM. If Winos are
indeed the dark matter, it will be highly advantageous from the point of view
of detection. If the halo density is dominated by the Wino-like LSP, the
detection rate of Wino CDM in Ge detectors can be as large as $0.1 - 0.01$
event/kg/day, which is within the reach of the future CDM detection with Ge
detector. Furthermore, there is a significant positron signal from pair
annihilation of Winos in our galaxy which should give a spectacular signal at
AMS.
