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Using the covariant formalism, we derive the equations of motion foradiabatic and entropy perturbations at third order in perturbation theory forcosmological models involving two scalar fields. We use these equations tocalculate the trispectrum of ekpyrotic and cyclic models in which the densityperturbations are generated via the entropic mechanism. In these models, theconversion of entropy into curvature perturbations occurs just before the bigbang, either during the ekpyrotic phase or during the subsequent kinetic energydominated phase. In both cases, we find that the non-linearity parametersf_{NL} and g_{NL} combine to leave a very distinct observational imprint.

Multifield Cosmological Perturbations at Third Order and the Ekpyrotic Trispectrum