  Many models of supersymmetry breaking, in the context of either supergravity
or superstring theories, predict the presence of particles with weak scale
masses and Planck-suppressed couplings. Typical examples are the scalar moduli
and the gravitino. Excessive production of such particles in the early Universe
destroys the successful predictions of nucleosynthesis. In particular, the
thermal production of these relics after inflation leads to a bound on the
reheating temperature, T_{RH} < 10^9 GeV. In this paper we show that the
non-thermal generation of these dangerous relics may be much more efficient
than the thermal production after inflation. Scalar moduli fields may be
copiously created by the classical gravitational effects on the vacuum state.
Consequently, the new upper bound on the reheating temperature is shown to be,
in some cases, as low as 100 GeV. We also study the non-thermal production of
gravitinos in the early Universe, which can be extremely efficient and overcome
the thermal production by several orders of magnitude, in realistic
supersymmetric inflationary models.
