We investigate whether the Affleck-Dine mechanism can produce sufficient
baryon number of the universe in the gauge-mediated SUSY breaking models, while
evading the cosmological moduli problem by late-time entropy production. We
find that the Q-ball formation renders the scenario very difficult to work,
irrespective of the detail mechanism of the entropy production.Comment: 11 pages, RevTeX, 5 postscript figures include