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 10 9 g. In minimal supergravity, the subsequent decay of evaporated gravitinos into cascades of non-equilibrium particles leads to the formation 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.