  We investigate the production of gravitinos in a cosmological background.
Gravitinos can be produced during preheating after inflation due to a combined
effect of interactions with an oscillating inflaton field and absence of
conformal invariance. In order to get insight on conformal properties of
gravitino we reformulate phenomenological supergravity in SU(2,2|1)-symmetric
way. The Planck mass and F- and D-terms appear via the gauge-fixed value of a
superfield that we call conformon. We find that in general the probability of
gravitino production is not suppressed by the small gravitational coupling.
This may lead to a copious production of gravitinos after inflation. Efficiency
of the new non-thermal mechanism of gravitino production is very sensitive to
the choice of the underlying theory. This may put strong constraints on certain
classes of inflationary models.
