Symmetries of Vector Perturbations during the de Sitter Epoch

We analyze the class of models where a suitable coupling between the inflaton field and the vector field gives rise to scale-invariant vector perturbations. We exploit the fact that the de Sitter isometry group acts as conformal group on the three-dimensional Euclidean space for the super-Hubble fluctuations in order to characterize the correlators involving the inflaton and the vector fields.