Moduli fields are generally present in superstring-inspired models. They are typically characterized by masses of the order of the supersymmetry breaking scale and by interactions of gravitational strength to ordinary matter. If stable, they can easily overclose the Universe. If unstable, strong limits on their abundance have to be imposed not to disrupt the successful predictions of nucleosynthesis. We discuss the production of moduli quanta from loops of cosmic strings, which may form at phase transitions in the early history of the Universe. As an application, we then focus on strings formed at the end of hybrid inflation, showing that in this case the coupling of the moduli to the field which forms the string network has to be much weaker than the typical gravitational interactions not to exceed the bounds from nucleosynthesis. Alternatively, if the relevant coupling is of gravitational order, an upper bound of about 10 13 GeV is imposed on the string energy scale.
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It is a pleasure to thank Antonio Riotto for bringing our attention to the problem and for interesting comments, and Gianmassimo Tasinato for collaboration at the early stages of the work. We acknowledge useful conversations with Robert Brandenberger, Stefan Groot Nibbelink, Lev Kofman, Patrick Peter, and Daniele Steer. We also thank Pierre Binétruy, Jose J. Blanco-Pillado, and Anne Davis for important comments on the earlier version of the paper. This work is partially supported by the European Community's Human Potential Programme under contract HPRN-CT-2000-00152 Supersymmetry and the Early Universe. M.P. also acknowledges support by the contracts HPRN-CT-2000-00131 and HPRN-CT-2000-00148.