Modulus D-term inflation

We propose a new model of single-field D-term inflation in supergravity, where the inflation is driven by a single modulus field which transforms non-linearly under the $U\left(1\right)$ gauge symmetry. One of the notable features of our modulus D-term inflation scenario is that the global $U\left(1\right)$ remains unbroken in the vacuum and hence our model is not plagued by the cosmic string problem which can exclude most of the conventional D-term inflation models proposed so far due to the CMB observations.