Solution of a Braneworld Big Crunch/Big Bang Cosmology

TL;DR

This paper analyzes cosmological perturbations in a five-dimensional brane-world model near a big crunch/big bang event, revealing limitations of four-dimensional effective theory at certain orders and exploring mode mixing during brane collision.

Contribution

It provides a detailed solution for perturbations in a five-dimensional brane collision scenario, highlighting the breakdown of 4D theory near singularities and mode interactions.

Findings

Four-dimensional effective theory fails at order (V/c)^2 near the singularity.

Mode mixing occurs between growing and decaying modes during brane separation.

The analysis offers insights into the cosmological implications of brane collisions.

Abstract

We solve for the cosmological perturbations in a five-dimensional background consisting of two separating or colliding boundary branes, as an expansion in the collision speed V divided by the speed of light c. Our solution permits a detailed check of the validity of four-dimensional effective theory in the vicinity of the event corresponding to the big crunch/big bang singularity. We show that the four-dimensional description fails at the first nontrivial order in (V/c)^2. At this order, there is nontrivial mixing of the two relevant four-dimensional perturbation modes (the growing and decaying modes) as the boundary branes move from the narrowly-separated limit described by Kaluza-Klein theory to the well-separated limit where gravity is confined to the positive-tension brane. We comment on the cosmological significance of the result and compute other quantities of interest in five-dimensional cosmological scenarios.