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 .