  We utilize a recently proposed cubic nilpotent superfield to realize
inflation in supergravity with the minimal degrees of freedom: the inflaton,
graviton, and massive gravitino. As an advantage, the resultant model is free
from the catastrophic production of gravitinos due to its vanishing propagation
speed. However, the model suffers from the standard gravitino problem, and its
viability depends on the mass spectrum and the thermal history of the universe.
