Mixed axion/gravitino dark matter from SUSY models with heavy axinos

We examine dark matter production rates in supersymmetric axion models typified by the mass hierarchy m_gravitino << m_neutralino << m_axino. In such models, one expects the dark matter to be composed of an axion/gravitino admixture. After presenting motivation for how such a mass hierarchy might arise, we examine dark matter production in the SUSY Kim-Shifman-Vainshtein-Zakharov (KSVZ) model, the SUSY Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) model and a hybrid model containing contributions from both KSVZ and DFSZ. Gravitinos can be produced thermally and also non-thermally from axino, saxion or neutralino decay. We obtain upper bounds on T_R due to overproduction of gravitinos including both the thermal and non-thermal processes. For T_R near the upper bound, then dark matter tends to be gravitino dominated, but for T_R well below the upper bounds, then axion domination is more typical although in many cases we find a comparable mixture of both axions and gravitinos. In this class of models, we ultimately expect detection of relic axions but no WIMP signal, although SUSY should ultimately be discovered at colliders.