Inflation with Massive Vector Fields

We investigate the coupling between the inflaton and massive vector fields. All renormalizable couplings with shift symmetry of the inflaton are considered. The massive vector can be decomposed into a scalar mode and a divergence-free vector mode. We show that the former naturally interacts with the inflaton and the latter decouples at tree level. The model in general predicts $f_{NL}^\mathrm{equil} = \mathcal{O}(1)$, while in some regions of the parameter space large non-Gaussianity can arise.