  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.
