Cosmology of supersymmetric models with low-energy gauge mediation

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 nontrivial 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 two-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 $\lesssim {(10\mathrm{}}^7$ $\mathrm{GeV}{)}^4$. 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.