Can thermal inflation be consistent with baryogenesis in gauge-mediated
  SUSY breaking models?
  Thermal inflation is an attractive idea to dilute cosmic density of unwanted
particles such as moduli fields which cause cosmological difficulties. However,
it also dilutes preexisting baryon asymmetry and some viable baryogenesis is
necessary for a cosmologically consistent scenario. We investigate whether the
Affleck-Dine mechanism can produce baryon asymmetry enough to survive after the
dilution in gauge-mediated SUSY breaking models. Flat directions except for
$LH_u$ flat direction cannot provide such huge baryon number because of Q-ball
formation. We show that although the $LH_u$ flat direction is special in terms
of having $\mu$-term which prevents Q-ball formation, it cannot explain the
observed baryon asymmetry either.
