| Summary: | Thermal Leptogenesis and the gravitino problem are reviewed in the framework of non-standard cosmologies. We consider in particular the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi mathvariant="script">T</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> cosmology, where <inline-formula> <math display="inline"> <semantics> <mi mathvariant="script">T</mi> </semantics> </math> </inline-formula> 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 to <inline-formula> <math display="inline"> <semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi mathvariant="script">T</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> cosmology, we shortly discuss also the case of the shear dominated Universe.
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