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.
