We discuss toy models where supersymmetry is broken due to non-vanishing
time-varying vacuum expectation value of the inflaton field during preheating.
We discuss the production of inflatino the superpartner of inflaton due to
vacuum fluctuations and then we argue that they do not survive until
nucleosynthesis and decay along with the inflaton to produce a thermal bath
after preheating. Thus the only relevant remnant is the helicity \pm 3/2
gravitinos which can genuinely cause problem to nucleosynthesis.Comment: 10 pages, Updates to match the accepted version in Phys. Rev.