Perturbations in a Bouncing Brane Model

TL;DR

This work analyzes how scalar perturbations evolve through a brane-brane collision in a five-dimensional Ekpyrotic/Cyclic cosmology within heterotic M-theory. By imposing boundedness of the Riemann tensor and energy-momentum and enforcing delta-function matching at the branes, the authors show that for generic near-bounce behavior (k ≥ 3) no nontrivial, bounded perturbation solution exists, effectively yielding a singular or ill-defined bounce. Only the special case of constant-velocity approach (k = 1) admits a consistent, non-singular perturbative solution, allowing explicit tracking of perturbations through the collision and enabling the transfer of a bulk, scale-invariant spectrum to the visible brane. These results indicate that the viability of Ekpyrotic/Cyclic scenarios hinges on the detailed dynamics of the brane collision and highlight the potential for a scale-invariant bulk spectrum to imprint on our universe if the bounce proceeds with constant brane velocity.

Abstract

The question of how perturbations evolve through a bounce in the Cyclic and Ekpyrotic models of the Universe is still a matter of ongoing debate. In this report we show that the collision between boundary branes is in most cases singular even in the full 5-D formalism, and that first order perturbation theory breaks down for at least one perturbation variable. Only in the case that the boundary branes approach each other with constant velocity shortly before the bounce, can a consistent, non singular solution be found. It is then possible to follow the perturbations explicitly until the actual collision. In this case, we find that if a scale invariant spectrum developed on the hidden brane, it will get transferred to the visible brane during the bounce.