Multifield Cosmological Perturbations at Third Order and the Ekpyrotic
  Trispectrum
  Using the covariant formalism, we derive the equations of motion for
adiabatic and entropy perturbations at third order in perturbation theory for
cosmological models involving two scalar fields. We use these equations to
calculate the trispectrum of ekpyrotic and cyclic models in which the density
perturbations are generated via the entropic mechanism. In these models, the
conversion of entropy into curvature perturbations occurs just before the big
bang, either during the ekpyrotic phase or during the subsequent kinetic energy
dominated phase. In both cases, we find that the non-linearity parameters
f_{NL} and g_{NL} combine to leave a very distinct observational imprint.
