Superconformal D-term inflation

We study models of hybrid inflation in the framework of supergravity with superconformal matter. F-term hybrid inflation is not viable since the inflaton acquires a large tachyonic mass. On the contrary, D-term hybrid inflation can successfully account for the amplitude of the primordial power spectrum. It is a two-field inflation model which, depending on parameters, yields values of the scalar spectral index down to n(s) similar or equal to 0.96. Generically, there is a tension between a small spectral index and the cosmic string bound albeit, within 2 sigma uncertainty, the current observational bounds can be simultaneously fulfilled.