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Thermal Leptogenesis and the gravitino problem are reviewed in the framework of non-standard cosmologies. We consider in particular thef ( T )cosmology, where    T    is the torsion field. We constrain the parameters space of these cosmological models consistently with thermal Leptogenesis scenario (with degenerate mass spectrum of light neutrinos), and we show that they allow to solve the gravitino problem as well. Owing to the similar characteristics tof ( T )cosmology, we shortly discuss also the case of the shear dominated Universe.

Consequences of f(?) Cosmology in Thermal Leptogenesis and Gravitino Late Abundance