Identification of perturbation modes and controversies in ekpyrotic perturbations

TL;DR

This paper clarifies the nature of perturbation modes in ekpyrotic cosmology, correcting previous misconceptions and controversies by accurately deriving the spectra using gauge-invariant methods without requiring joining conditions.

Contribution

It provides a consistent derivation of the perturbation spectra in ekpyrotic scenarios and corrects prior errors related to mode identification and joining conditions.

Findings

Surviving fluctuations have very blue spectra with suppressed amplitude.

Previous claims of scale-invariance were based on incorrect mode interpretation.

No joining condition is necessary for the derivation.

Abstract

If the linear perturbation theory is valid through the bounce, the surviving fluctuations from the ekpyrotic scenario (cyclic one as well) should have very blue spectra with suppressed amplitude for the scalar-type structure. We derive the same (and consistent) result using the curvature perturbation in the uniform-field (comoving) gauge and in the zero-shear gauge. Previously, Khoury et al. interpreted results from the latter gauge condition incorrectly and claimed the scale-invariant spectrum, thus generating controversy in the literature. We also correct similar errors in the literature based on wrong mode identification and joining condition. No joining condition is needed for the derivation.