In the context of a conformal Supergravity (SUGRA) model in the Einstein frame, in which the (next to) minimal supersymmetric standard model can embedded naturally to produce chaotic inflation scenarios, we study properties of gravitino in the cases where it is stable or unstable. In the latter case, we demonstrate that for large dilaton scale factors there is an enhanced magnitude of the gravitino width, when it decays to neutralino dark matter, as compared with the standard SUGRA case. In this context, we discuss the associated consequences as far as Big Bang Nucleosynthesis constraints and avoidance of gravitino overproduction are concerned.

7 pages latex, two eps figures incorporated