The Suyama-Yamaguchi consistency relation in the presence of vector
  fields
  We consider inflationary models in which vector fields 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 is generated due to the superhorizon
evolution, we use the \delta N formalism to do a complete tree level
calculation of the non-Gaussianity parameters f_{NL} and \tau_{NL} in the
presence of vector fields. We isolate the isotropic pieces of the
non-Gaussianity parameters, which anyway have contributions from the vector
fields, and show that they obey the Suyama-Yamaguchi consistency relation
\tau^{iso}_{NL}>=(6/5f^{iso}_{NL})^2. Other ways of defining the
non-Gaussianity parameters, which could be observationally relevant, are stated
and the respective Suyama-Yamaguchi-like consistency relations are obtained.
