Inflation in uplifted Supergravities

We present a model of slow-roll inflation in the context of effective Supergravities arising from string theories. The uplifting of the potential (to generate dS or Minkowski vacua) is provided by the D-term associated to an anomalous U(1), in a fully consistent and gauge invariant formulation. We develop a minimal working model which incorporates eternal topological inflation and complies with observational constraints, avoiding the usual obstacles to implement successful inflation ("eta problem" and initial condition problem among others).