Cosmological Perturbations in a Big Crunch/Big Bang Space-time

TL;DR

This paper presents a method for matching cosmological perturbations across singularities in cyclic universe models, demonstrating that scale-invariant perturbations can pass through the big crunch/big bang transition.

Contribution

A new gauge-based prescription for matching relativistic perturbations across singularities in cyclic cosmologies is introduced, extending previous mode-matching techniques.

Findings

Long wavelength perturbations remain scale-invariant after the transition.

Perturbations in the incoming state pass through the singularity and grow in the expanding phase.

The method applies to models with orbifold collision singularities.

Abstract

A prescription is developed for matching general relativistic perturbations across singularities of the type encountered in the ekpyrotic and cyclic scenarios i.e. a collision between orbifold planes. We show that there exists a gauge in which the evolution of perturbations is locally identical to that in a model space-time (compactified Milne mod Z_2) where the matching of modes across the singularity can be treated using a prescription previously introduced by two of us. Using this approach, we show that long wavelength, scale-invariant, growing-mode perturbations in the incoming state pass through the collision and become scale-invariant growing-mode perturbations in the expanding hot big bang phase.