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We consider inflationary models in which vector fields are responsible forpart or eventually all of the primordial curvature perturbation \zeta. Suchmodels are phenomenologically interesting since they naturally introduceanisotropies in the probability distribution function of the primordialfluctuations that can leave a measurable imprint in the cosmic microwavebackground. Assuming that non-Gaussianity is generated due to the superhorizonevolution, we use the \delta N formalism to do a complete tree levelcalculation of the non-Gaussianity parameters f_{NL} and \tau_{NL} in thepresence of vector fields. We isolate the isotropic pieces of thenon-Gaussianity parameters, which anyway have contributions from the vectorfields, and show that they obey the Suyama-Yamaguchi consistency relation\tau^{iso}_{NL}>=(6/5f^{iso}_{NL})^2. Other ways of defining thenon-Gaussianity parameters, which could be observationally relevant, are statedand the respective Suyama-Yamaguchi-like consistency relations are obtained.

The Suyama-Yamaguchi consistency relation in the presence of vector fields