  The Large Volume Scenario for getting a non-supersymmetric vacuum in type IIB
string theory leads, through the Weyl anomaly and renormalization group
running, to an interesting phenomenology. However, for gravitino masses below
500 TeV there are cosmological problems and the resulting Higgs mass is well
below 124 GeV. Here we discuss the phenomenology and cosmology for gravitino
masses which are $\gtrsim$ 500 TeV. We find that not only is the cosmological
modulus problem alleviated and the right value for dark matter density
obtained, but also the Higgs mass is in the 122-125 GeV range. However the
spectrum of SUSY particles will be too heavy to be observed at the LHC.
