S. N. Nakamura

Gravitino production from heavy moduli decay and cosmological moduli problem revived

Abstract 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 10 5 GeV . Furthermore to avoid the over-abundance of the stable neutralino lightest superparticles (LSPs), the gravitino must weigh more than about 10 6 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.

Gravitinos from heavy scalar decay

Cosmological issues of the gravitino production by the decay of a heavy scalar field

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are examined, assuming that the damped coherent oscillation of the scalar once dominated the energy of the universe. The coupling of the scalar field to a gravitino pair is estimated both in spontaneous and explicit supersymmetry breaking scenarios, with the result that it is proportional to the vacuum expectation value of the scalar field in general. Cosmological constraints depend on whether the gravitino is stable or not, and we study each case separately. For the unstable gravitino with

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decay, in order to retain the success of the big-bang nucleosynthesis. It is also shown that it severely constrains the decay rate into the gravitino pair. For the stable gravitino, similar but less stringent bounds are obtained to escape the overclosure by the gravitinos produced at the

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decay. The requirement that the free-streaming effect of such gravitinos should not suppress the cosmic structures at small scales eliminates some regions in the parameter space, but still opens a new window for the gravitino warm dark matter. Implications of these results to inflation models are discussed. In particular, it is shown that modular inflation will face serious cosmological difficulty when the gravitino is unstable, whereas it can escape the constraints for the stable gravitino. A similar argument offers a solution to the cosmological moduli problem, in which the moduli is relatively heavy while the gravitino is light.