  Gravitinos can inherit a non-relativistic dispersion relation while
propagating in a background breaking both supersymmetry and Lorentz symmetry
spontaneously. This is because the longitudinal mode velocity is controlled by
the sound speed in the background. It was pointed out recently by Kolb, Long
and McDonough that the production of gravitinos might diverge when this sound
speed vanishes. We argue that in the framework of cosmological models with
linearly spontaneously broken realised supersymmetry, where the physical
fermions are combinations of the vacuum goldstino and the inflatino, the
gravitino longitudinal mode has a relativistic dispersion relation and
therefore avoids the catastrophic production. We illustrate this in some
explicit examples.
