THE SUYAMA-YAMAGUCHI CONSISTENCY RELATION IN THE PRESENCE OF VECTOR FIELDS

We consider inflationary models in which vector fields (VF) are responsible for part or eventually all of the primordial curvature perturbation zeta. Such models are phenomenologically interesting since they naturally introduce anisotropies in the probability distribution function of the primordial fluctuations that can leave a measurable imprint in the cosmic microwave background. Assuming that non-Gaussianity (NG) is generated due to the superhorizon evolution, we use the delta N formalism to do a complete tree level calculation of the NG parameters f(NL) and tau(NL) in the presence of VF. We isolate the isotropic pieces of the NG parameters, which anyway have contributions from the VF, and show that they obey the Suyama-Yamaguchi (SY) consistency relation iso NL=(65fisoNL)2.Other waysofdefiningtheNGparameters,whichcouldbeobservationallyrelevant,arestated andtherespectiveSY-likeconsistencyrelationsareobtained