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 inflati onary scenario can naturally emerge in theories with non-anomalous or anomalous U(1) gauge symmetry. In the latter case the scale of inflati on is fixed by the Green-Schwarz mechanism of anomaly cancellation. Th e crucial point is that the (super)gravity-mediated curvature of all t he scalar fields (and, in particular, of the inflaton), which in the s tandard F-dominated case is of the order of the Hubble parameter, is a bsent in the D-term inflation case. The curvature of moduli and of all other flat directions during such an inflation crucially depends on t heir gauge charges.