The R Axion From Dynamical Supersymmetry Breaking

All generic, calculable models of dynamical supersymmetry breaking have a spontaneously broken $R$ symmetry and therefore contain an $R$ axion. We show that the axion is massive in any model in which the cosmological constant is fine-tuned to zero through an explicit $R$-symmetry-breaking constant. In visible-sector models, the axion mass is in the 100 MeV range and thus evades astrophysical bounds. In nonrenormalizable hidden-sector models, the mass is of order of the weak scale and can have dangerous cosmological consequences similar to those already present from other fields. In renormalizable hidden- sector models, the axion mass is generally quite large, of order $10^7$ GeV. Typically, these axions are cosmologically safe. However, if the dominant decay mode is to gravitinos, the potentially large gravitino abundance that arises from axion decay after inflation might affect the successful predictions of big-bang nucleosynthesis. We show that the upper bound on the reheat temperature after standard inflation can be competitive with or stronger than bounds from thermal gravitino production, depending on the model and the gravitino mass.