Multifield Cosmological Perturbations at Third Order and the Ekpyrotic Trispectrum

TL;DR

This paper derives third-order equations for cosmological perturbations in two-field models and calculates the trispectrum, revealing distinctive non-Gaussian signatures in ekpyrotic and cyclic scenarios.

Contribution

It introduces a covariant formalism for third-order perturbations and computes the trispectrum for ekpyrotic models with entropy-to-curvature conversion.

Findings

Distinct non-Gaussian signatures in the trispectrum.

Non-linearity parameters f_{NL} and g_{NL} have unique observational imprints.

The formalism applies to models with entropy conversion before the big bang.

Abstract

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.