We discuss some cosmological problems in supersymmetry and supergravity. First, we present (chaotic, hybrid and new) inflation models based on supergravity.. Then we consider the serious problem due to thermally and non-thermally produced gravitinos and show that it gives severe constraints on the reheating temperature and the inflaton properties. Finally the supersymmetric axion model is studied and it is shown that overproduction of saxions and axinos sets more stringent upper limit on the reheating temperature than overproduction of the gravitinos.
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