D-term inflation in superstring theories

An inflationary stage dominated by a D-term avoids the slow-roll problem of inflation in supergravity and may emerge in theories with a non-anomalous or anomalous U(1) gauge symmetry. The most intriguing and commonly invoked possibility is that the Fayet-Iliopoulos D-term triggering inflation is the one emerging in superstring theories. We discuss the complications one has to face when trying to build up a successful D-term inflationary scenario in superstring models. In particular, we show that the ``vacuum shifting'' phenomenon of string theories is usually very efficient even in the early Universe, thus preventing inflation from taking place. On the other hand, when D-term inflation is free to occur, the presence of a plethora of fields and several non-anomalous additional Abelian symmetries in string theories may help in reconciling the value of the Fayet-Iliopoulos D-term required by the COBE normalization with the value predicted by string theories. We also show that in superstring D-term inflation gravitinos are likely to pose no cosmological problem.