D-Term Inflation
  We show that inflation which is dominated by the D-term density avoids the `slow-roll' problem of inflation in supergravity. Such an inflationary scenario can naturally emerge in theories with non-anomalous or anomalous U(1) gauge symmetry. In the latter case the scale of inflation is fixed by the Green--Schwarz mechanism of anomaly cancellation. The crucial point is that the (super)gravity-mediated curvature of all the scalar fields (and, in particular, of the inflaton), which in the standard F-dominated case is of the order of the Hubble parameter, is absent in the D-term inflation case. The curvature of moduli and of all other flat directions during such an inflation crucially depends on their gauge charges. 
Pierre Binetruy and Gia Dvali