Baryogenesis and gravitino dark matter in gauge-mediated supersymmetry-breaking models

We discuss two cosmological issues in a generic gauge-mediated supersymmetry~SUSY-!breaking model, namely, the Universe’s baryon asymmetry and the gravitino dark-matter density. We show that both problems can be simultaneously solved if there exist extra matter multiplets of a SUSY-invariant mass of the order of the ‘‘m term,’’ as suggested in several realistic SUSY grand-unified theories. We propose an attractive scenario in which the observed baryon asymmetry is produced in a way totally independent of the reheating temperature of inflation without causing any cosmological gravitino problem. Furthermore, in a relatively wide parameter space, we can also explain the present mass density of cold dark matter by the thermal relics of the gravitinos without an adjustment of the reheating temperature of inflation. We point out that there is an interesting relation between the baryon asymmetry and the dark-matter density.