  We have proposed recently a framework for inflation driven by supersymmetry
breaking with the inflaton being a superpartner of the goldstino, that avoids
the main problems of supergravity inflation, allowing for: naturally small
slow-roll parameters, small field initial conditions, absence of a
(pseudo)scalar companion of the inflation, and a nearby minimum with tuneable
cosmological constant. It contains a chiral multiplet charged under a gauged
R-symmetry which is restored at the maximum of the scalar potential with a
plateau where inflation takes place. The effective field theory relies on two
phenomenological parameters corresponding to corrections to the K\"ahler
potential up to second order around the origin. The first guarantees the
maximum at the origin and the second allows the tuning of the vacuum energy
between the F- and D-term contributions. Here, we provide a microscopic model
leading to the required effective theory. It is a Fayet-Iliopoulos model with
two charged chiral multiplets under a second U(1) R-symmetry coupled to
supergravity. In the Brout-Englert-Higgs phase of this U(1), the gauge field
becomes massive and can be integrated out in the limit of small supersymmetry
breaking scale. In this work, we perform this integration and we show that
there is a region of parameter space where the effective supergravity realises
our proposal of small field inflation from supersymmetry breaking consistently
with observations and with a minimum of tuneable energy that can describe the
present phase of our Universe.
