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 nonlinearity parameters $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ combine to leave a very distinct observational imprint.

• Received 12 June 2009

DOI:https://doi.org/10.1103/PhysRevD.80.063503