The moduli and gravitino (non)-problems in models with strongly stabilized moduli

In gravity mediated models and in particular in models with strongly stabilized moduli, there is a natural hierarchy between gaugino masses, the gravitino mass and moduli masses: m1/2 << m3/2 << mφ. Given this hierarchy, we show that 1) moduli problems associated with excess entropy production from moduli decay and 2) problems associated with moduli/gravitino decays to neutralinos are non-existent. Placed in an inflationary context, we show that the amplitude of moduli oscillations are severely limited by strong stabilization. Moduli oscillations may then never come to dominate the energy density of the Universe. As a consequence, moduli decay to gravitinos and their subsequent decay to neutralinos need not overpopulate the cold dark matter density.