Non-Gaussianities in extended D-term inflation

We explore extensions of hybrid inflationary models in the context of supersymmetric D-term inflation. We point out that a large variety of inflationary scenarios can be encountered when the field content is extended. It is not only possible to get curvaton type models but also scenarios in which different fields, with nontrivial statistical properties, contribute to the primordial curvature fluctuations. We explore more particularly the parameter space of these multiple-field inflationary models. It is shown that there exists a large domain in which significant primordial non-Gaussianities can be produced while preserving a scale free power spectrum for the metric fluctuations. In particular we explicitly compute the expected bispectrum and trispectrum for such models and compared the results to the current and expected observational constraints. It is shown that it is necessary to use both the bispectra and trispectra of cosmic microwave background anisotropies to efficiently reduce their parameter space.