Dilaton and Moduli Fields in D-term inflation

We investigate the possibility of $D$-term inflation within the framework of type I string-inspired models. Although $D$-term inflation model has the excellent property that it is free from the so-called $\eta$- problem, two serious problems appear when we embed $D$-term inflation in string theory, the magnitude of FI term and the rolling motion of the dilation. In the present paper, we analyze the potential of $D$-term inflation in type I inspired models and study the behavior of dilaton and twisted moduli fields. Adopting the non-perturbative superpotential induced by gaugino condensation, the twisted moduli can be stabilized. If the dilaton is in a certain range, it evolves very slowly and does not run away to infinity. Thus $D$-term dominated vacuum energy becomes available for driving inflation. By studying the density perturbation generated by the inflation model, we derive the constraints on model parameters and give some implications on $D$-term inflation in type I inspired models.