Gravitino Production from Heavy Moduli Decay and Cosmological Moduli Problem Revived

The cosmological moduli problem for relatively heavy moduli fields is reinvestigated. For this purpose we examine the decay of a modulus field at a quantitative level. The modulus dominantly decays into gauge bosons and gauginos, provided that the couplings among them are not suppressed in the gauge kinetic function. Remarkably the modulus decay into a gravitino pair is unsuppressed generically, with a typical branching ratio of order 0.01. Such a large gravitino yield after the modulus decay causes cosmological difficulties. The constraint from the big-bang nucleosynthesis pushes up the gravitino mass above 105 GeV. Furthermore to avoid the over-abundance of the stable neutralino lightest superparticles (LSPs), the gravitino must weigh more than about 106 GeV for the wino-like LSP, and even more for other neutralino LSPs. This poses a stringent constraint on model building of low-energy supersymmetry.