  We study the cosmology of supersymmetric models in which the supersymmetry
breaking effects are mediated by gauge interactions at about the 10^5 GeV
scale. We first point out that the gravitino is likely to overclose the
Universe in this class of models. This requires an entropy production, which
prefers a baryogenesis mechanism at a relatively low temperature. The
Affleck-Dine mechanism for baryogenesis is one of the possibilities to generate
enough baryon asymmetry, but the analysis is non-trivial since the shape of the
potential for the flat direction differs substantially from the conventional
hidden sector case. To see this, we first perform a 2-loop calculation to
determine the shape of the potential. By combining the potential with the
supergravity contribution, we then find that the Affleck-Dine baryogenesis
works efficiently to generate sufficient baryon asymmetry. On the other hand,
we also point out that string moduli fields, if present, are stable and their
coherent oscillations overclose the Universe by more than 15 orders of
magnitude. One needs a very late inflationary period with an e-folding of N
\gtrsim 5 and an energy density of \lesssim (10^7 GeV)^4. A thermal inflation
is enough for this purpose. Fortunately, the Affleck-Dine baryogenesis is so
efficient that enough baryon asymmetry can survive the late inflation.
