Massive vector multiplet with Dirac-Born-Infeld and new Fayet-Iliopoulos terms in supergravity

We propose a four-dimensional N = 1 supergravity-based Starobinsky-type inflationary model in terms of a single massive vector multiplet, whose action includes the Dirac-Born-Infeld-type kinetic terms and a generalized (new) Fayet-Iliopolulos-type term without gauging the R-symmetry. The bosonic action and the scalar potential are computed. Inflaton is the superpartner of goldstino in our model, and supersymmetry is spontaneously broken after inflation by the D-type mechanism, whose scale is related to the value of the cosmological constant.