The gravitino problem in Extended Gravity cosmologies

The gravitino problem is investigated in the framework of Extended Gravity cosmologies. In particular, we consider $f(R)$ gravity, the most natural extension of the Hilbert-Einstein action, and $f(\cal T)$ gravity, the extension of teleparallel equivalent gravity. Since in these theories the expansion laws of the Universe are modified, as compared to the standard $\Lambda$CDM cosmology, it follows that also the thermal history of particles gets modified. We show that $f(R)$ models allow to avoid the late abundance of gravitinos. In particular, we found that for an appropriate choice of the parameters characterizing the $f(R)$ model, the gravitino abundance turns out to be independent of the reheating temperature. A similar behavior is achieved also in the context of $f(\cal T)$ gravity. In this perspective, we can conclude that geometric corrections to standard General Relativity (and to Teleparallel Equivalent of General Relativity) can improve shortcomings both in cosmology and in unified theories beyond the Standard Model of particles.