Comments on D-term inflation

An inflationary stage dominated by a D-term avoids the slow-roll problem of inflation in supergravity and can naturally emerge in theories with a non-anomalous or anomalous U(1) gauge symmetry. In the latter case, however, the scale of inflation as imposed by the COBE normalization is in contrast with the value fixed by the Green-Schwarz mechanism of anomaly cancellation. In this paper we discuss possible solutions to this problem and comment about the fact that the string-loop generated Fayet-Iliopoulos D-term may trigger the presence of global and local cosmic strings at the end of inflation.