Non-Gaussianities in extended D-term inflation

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I will present extensions of hybrid inflationary models in the context of supersymmetric D-term in- flation. I will show that there exists a large domain of parameters in which significant primordial non-Gaussianities can be produced while preserving a scale free power spectrum for the metric fluctuations. In particular I will explicitly present the expected bi- and trispectrum for such models and compared the results to the current and expected observational constraints. It is to be noticed that it is necessary to use both the bi- and tri-spectra of CMB anisotropies to efficiently reduce the parameter space of such models.