Double D-term inflation
  Comparisons of cosmological models to current data show that the presence of a non-trivial feature in the primordial power spectrum of fluctuations, around the scale k=0.05 h/Mpc, is an open and exciting possibility, testable in a near future. This could set new constraints on inflationary models. In particular, current data favour a Lambda-CDM model with a steplike spectrum, and more power on small scales. So far, this possibility has been implemented only in toy models of inflation. In this work, we propose a supersymmetric model with two U(1) gauge symmetries, associated with two Fayet-Iliopoulos terms. Partial cancellation of the Fayet-Iliopoulos by one of the charged fields generates a step in the primordial power spectrum of adiabatic perturbations. We show that when this field if charged under both symmetries, the spectrum may have more power on small scales. 
Julien Lesgourgues (SISSA)