The failure of cosmological perturbation theory in the new ekpyrotic and cyclic ekpyrotic scenarios

TL;DR

The paper challenges the viability of generating the observed curvature perturbation ${\cal R}$ in the new and cyclic ekpyrotic scenarios by showing that linear cosmological perturbation theory breaks down near the bounce. It analyzes the ek3 calculation, derives the Bardeen-potential spectrum ${\cal P}_{\Phi}^{1/2}$ during the collapsing phase, and highlights the implicit cross-bounce matching that assumes linear evolution. A central result is that, as the singularity is approached, either the density contrast or ${\cal R}$ diverges in any gauge, rendering the linear perturbation equations inapplicable and invalidating the claimed flat ${\cal R}$ spectrum produced by this mechanism. Consequently, generating the observed curvature perturbation in these scenarios likely requires non-linear treatment or alternative mechanisms (e.g., a curvaton with noncanonical kinetics), underscoring a significant challenge to bounce-based perturbation generation and highlighting the comparative robustness of inflationary predictions for ${\cal R}$.

Abstract

Cosmological perturbation theory fails in the new ekpyrotic and cyclic ekpyrotic scenarios, before the scale factor of the Universe reaches zero. As a result, a recently-proposed recipe for evolving the curvature perturbation through the bounce in these scenarios cannot be justified.