  We investigate non-thermal gravitino production after tribrid inflation in
supergravity, which is a variant of supersymmetric hybrid inflation where three
fields are involved in the inflationary model and where the inflaton field
resides in the matter sector of the theory. In contrast to conventional
supersymmetric hybrid inflation, where non-thermal gravitino production imposes
severe constraints on the inflationary model, we find that the "non-thermal
gravitino problem" is generically absent in models of tribrid inflation, mainly
due to two effects: (i) With the inflaton in tribrid inflation (after
inflation) being lighter than the waterfall field, the latter has a second
decay channel with a much larger rate than for the decay into gravitinos. This
reduces the branching ratio for the decay of the waterfall field into
gravitinos. (ii) The inflaton generically decays later than the waterfall
field, and does not produce gravitinos when it decays. This leads to a dilution
of the gravitino population from the decays of the waterfall field. The
combination of both effects generically leads to a strongly reduced gravitino
production in tribrid inflation.
