Affleck-Dine Baryogenesis, Condensate Fragmentation and Gravitino Dark Matter in Gauge-Mediation with a Large Messenger Mass

We study the conditions for successful Affleck-Dine baryogenesis and the origin of gravitino dark matter in GMSB models. AD baryogenesis in GMSB models is ruled out by neutron star stability unless Q-balls are unstable and decay before nucleosynthesis. Unstable Q-balls can form if the messenger mass scale is larger than the flat-direction field Phi when the condensate fragments. We provide an example based on AD baryogenesis along a d = 6 flat direction for the case where m_{3/2} \approx 2 GeV, as predicted by gravitino dark matter from Q-ball decay. Using a phenomenological GMSB potential which models the Phi dependence of the SUSY breaking terms, we numerically solve for the evolution of Phi and show that the messenger mass can be sufficiently close to the flat-direction field when the condensate fragments. We compute the corresponding reheating temperature and the baryonic charge of the condensate fragments and show that the charge is large enough to produce late-decaying Q-balls which can be the origin of gravitino dark matter.