Massive vector multiplet inflation with Dirac-Born-Infeld type action

We investigate the inflation model with a massive vector multiplet in a case that the action of the vector multiplet is extended to the Dirac-Born-Infeld (DBI) type one. We show the massive DBI action in four-dimensional N=1 supergravity and find that the higher-order corrections associated with the DBI extension make the scalar potential flat with a simple choice of the matter couplings. We also discuss the DBI extension of the new minimal Starobinsky model and find that it is dual to a special class of the massive DBI action.