  In supergravity, the dynamics of the sgoldstino -- superpartner of the
goldstino superfield associated with the breaking of supersymmetry at low
energy -- can substantially modify the dynamics of inflation in the primordial
Universe. So-called sgoldstinoless models assume the existence of a nilpotency
constraint $S^2=0$ that effectively removes the sgoldstino from the theory.
Such models were proposed to realise non-oscillatory inflation scenarios with a
single scalar field, which feature a long period of kination at the end of
inflation, and therefore a non-standard post-inflationary cosmology. Using
effective operators, we propose models in which the sgoldstino is stabilized
close to the origin to reproduce the nilpotent constraint. We show that small
sgoldstino fluctuations may lead to a sizeable back-reaction on the
cosmological history. We study the effect of this back-reaction on the
inflation observables measured in the cosmic microwave background and confront
the model to a series of constraints including limits on $\Delta N_{\rm eff}$.
We show that the peculiar form of the potential in the large supersymmetry
breaking scale limit can generate peaks in the scalar power spectrum produced
from inflation. We study how certain perturbation modes may re-enter the
horizon during or after kination and show that a large supersymmetry breaking
scale may lead to the formation of primordial black holes with various masses
in the early Universe.
