  We explain the motivation and main results of our work in reference
arXiv:0906.0530 [hep-th]. 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, and
use these equations to calculate the trispectrum of ekpyrotic and cyclic
models. The non-linearity parameters $f_{NL}$ and $g_{NL}$ are found to combine
to leave a very distinct observational imprint.
