On the axion, dilaton, Polonyi, gravitino and shadow matter problems in supergravity and superstring models

Any of the particles listed in the title may cause a cosmological problem for supergravity or superstring models, either by producing too much entropy when they decay, or by not decaying and leaving too much relic energy density in the Universe today. It is shown that the dilaton, axion, Polonyi and gravitino problems are essentially equivalent in a wide class of superstring models, and that no problems arise with cosmological nucleosynthesis if msub(3/2) > or approx. 104 GeV, or with baryosynthesis if msub(3/2) > or approx. 1013 GeV. If these problems are solved, shadow matter also decays harmlessly in the very early Universe. Attention is drawn to a class of phenomenological superstring models which avoid all these cosmological difficulties. (orig.)