Gravitino production by primordial black hole evaporation and constraints on the inhomogeneity of the early universe

In supergravity models, the evaporation of light primordial black holes should be a source of gravitinos. By considering this process, new stringent limits are derived on the abundance of small black holes with initial masses less than 109 g. In minimal supergravity, the subsequent decay of evaporated gravitinos into cascades of non-equilibrium particles leads to the fort-nation of elements whose abundance is constrained by observations. In gauge mediated supersymmetry breaking models, their density is required not to overclose the universe. As a result, cosmological models with substantial inhomogeneities on small scales are excluded.