Perturbations in a Bouncing Brane Model

TL;DR

This paper investigates the evolution of cosmological perturbations through a brane collision bounce, finding that most cases are singular, but a special constant velocity scenario allows for a consistent transfer of scale-invariant spectra.

Contribution

It demonstrates conditions under which perturbations can be consistently evolved through a brane collision in a 5-D model, highlighting a specific scenario with non-singular behavior.

Findings

Most brane collisions are singular in 5-D formalism.

First order perturbation theory breaks down near the bounce.

A constant velocity approach allows perturbation transfer of scale-invariant spectra.

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.